Skill based
Sorry for the length of this. What about simply using the existing 5E mechanic for ability check skills and basing psionics on 6 Wisdom skills, each with a group of "powers" that the psion can learn? Note: not fleshed out or balanced via playtest.
D&D 5E Psionics
6 Skills: Telepathy, Psychometabolism, Psychoportation, Psychokinesis, Clairsentience, and Metacreation
Within each skill, 6 minor powers, 3 major powers, and 1 true power
Cost of skill use is 1 for minor powers, 2 for major powers, and 4 for true powers
Recover all power points after a long rest.
Once per day, recover 1/3rd level (round up) after a short rest.
All skills are Wisdom skills. DC 0 for Innate, 10 for Minor, 15 for Major, and 20 for True.
Begin play knowing 1 skill, 0 true power, 0 major powers, and 3 minor powers.
Innate mental powers are the equivalent of cantrips. Zero power point cost to use them. Begin play knowing 3. You do not have to know a skill before learning an innate for that skill. Total of 3 innates per skill.
Psionicist (1d8)
[TABLE="width: 587"][TR][TD]Level
[/TD][TD]Prof
[/TD][TD]Special
[/TD][TD]PPs
[/TD][TD]Innate
[/TD][TD]Skills
[/TD][TD]Minor
[/TD][TD]Major
[/TD][TD]True
[/TD][/TR][TR][TD]1
[/TD][TD]+2
[/TD][TD]PP Recovery, Skill Focus
[/TD][TD]3
[/TD][TD]3
[/TD][TD]1
[/TD][TD]3
[/TD][TD]0
[/TD][TD]0
[/TD][/TR][TR][TD]2
[/TD][TD]+2
[/TD][TD]--
[/TD][TD]4
[/TD][TD]3
[/TD][TD]2
[/TD][TD]4
[/TD][TD]1
[/TD][TD]0
[/TD][/TR][TR][TD]3
[/TD][TD]+2
[/TD][TD]Mind Focus
[/TD][TD]5
[/TD][TD]3
[/TD][TD]2
[/TD][TD]4
[/TD][TD]1
[/TD][TD]0
[/TD][/TR][TR][TD]4
[/TD][TD]+2
[/TD][TD]Ability Score Increase
[/TD][TD]6
[/TD][TD]4
[/TD][TD]2
[/TD][TD]5
[/TD][TD]2
[/TD][TD]0
[/TD][/TR][TR][TD]5
[/TD][TD]+3
[/TD][TD]--
[/TD][TD]7
[/TD][TD]4
[/TD][TD]2
[/TD][TD]5
[/TD][TD]2
[/TD][TD]0
[/TD][/TR][TR][TD]6
[/TD][TD]+3
[/TD][TD]Mind Focus Ability
[/TD][TD]8
[/TD][TD]4
[/TD][TD]3
[/TD][TD]6
[/TD][TD]3
[/TD][TD]1
[/TD][/TR][TR][TD]7
[/TD][TD]+3
[/TD][TD]--
[/TD][TD]9
[/TD][TD]4
[/TD][TD]3
[/TD][TD]6
[/TD][TD]3
[/TD][TD]1
[/TD][/TR][TR][TD]8
[/TD][TD]+3
[/TD][TD]Ability Score Increase
[/TD][TD]10
[/TD][TD]4
[/TD][TD]3
[/TD][TD]7
[/TD][TD]4
[/TD][TD]1
[/TD][/TR][TR][TD]9
[/TD][TD]+4
[/TD][TD]--
[/TD][TD]11
[/TD][TD]4
[/TD][TD]3
[/TD][TD]7
[/TD][TD]4
[/TD][TD]1
[/TD][/TR][TR][TD]10
[/TD][TD]+4
[/TD][TD]Mind Focus Ability
[/TD][TD]12
[/TD][TD]5
[/TD][TD]4
[/TD][TD]8
[/TD][TD]5
[/TD][TD]1
[/TD][/TR][TR][TD]11
[/TD][TD]+4
[/TD][TD]--
[/TD][TD]13
[/TD][TD]5
[/TD][TD]4
[/TD][TD]8
[/TD][TD]5
[/TD][TD]2
[/TD][/TR][TR][TD]12
[/TD][TD]+4
[/TD][TD]Ability Score Increase
[/TD][TD]14
[/TD][TD]5
[/TD][TD]4
[/TD][TD]9
[/TD][TD]6
[/TD][TD]2
[/TD][/TR][TR][TD]13
[/TD][TD]+5
[/TD][TD]--
[/TD][TD]15
[/TD][TD]5
[/TD][TD]4
[/TD][TD]9
[/TD][TD]6
[/TD][TD]2
[/TD][/TR][TR][TD]14
[/TD][TD]+5
[/TD][TD]Mind Focus Ability
[/TD][TD]16
[/TD][TD]5
[/TD][TD]5
[/TD][TD]10
[/TD][TD]7
[/TD][TD]2
[/TD][/TR][TR][TD]15
[/TD][TD]+5
[/TD][TD]--
[/TD][TD]17
[/TD][TD]5
[/TD][TD]5
[/TD][TD]10
[/TD][TD]7
[/TD][TD]2
[/TD][/TR][TR][TD]16
[/TD][TD]+5
[/TD][TD]Ability Score Increase
[/TD][TD]18
[/TD][TD]5
[/TD][TD]5
[/TD][TD]11
[/TD][TD]8
[/TD][TD]3
[/TD][/TR][TR][TD]17
[/TD][TD]+6
[/TD][TD]--
[/TD][TD]19
[/TD][TD]5
[/TD][TD]5
[/TD][TD]11
[/TD][TD]8
[/TD][TD]3
[/TD][/TR][TR][TD]18
[/TD][TD]+6
[/TD][TD]Enhanced Recovery
[/TD][TD]20
[/TD][TD]5
[/TD][TD]6
[/TD][TD]12
[/TD][TD]9
[/TD][TD]3
[/TD][/TR][TR][TD]19
[/TD][TD]+6
[/TD][TD]Ability Score Increase
[/TD][TD]21
[/TD][TD]5
[/TD][TD]6
[/TD][TD]12
[/TD][TD]9
[/TD][TD]3
[/TD][/TR][TR][TD]20
[/TD][TD]+6
[/TD][TD]True Manifestation
[/TD][TD]22
[/TD][TD]5
[/TD][TD]6
[/TD][TD]13
[/TD][TD]10
[/TD][TD]3
[/TD][/TR][/TABLE]
Proficiencies: Light Armor, Shields, Rapier, Short Sword, Dagger, Quarterstaff, Light Crossbow
Note: Metal Armor interferes with the manifestation of psionic abilities, resulting in a +5 to the activation DC. Proficiency with armors of various types does not negate this penalty. Psionically active or magical metallic armor does not impose this DC penalty.
Power DC: 8 + Proficiency Bonus + Wisdom Modifier
PP Recovery: Once per day, you can regain power points equal to 1/3rd you manifesting level (round up) after a short rest.
Skill Focus: After each long rest, you choose one of the psionic skills that you are proficient with. You gain a +5 bonus to skills checks when manifesting powers from this skill.
Mind Focus: The first skill that you select becomes a mental focus for you, granting certain special abilities as you level.
Telepathy
3rd: Insert special ability here
6th: Insert special ability here
10th: Insert special ability here
14th: Insert special ability here
etc. (one list for each skill)
Enhanced Recovery: Once per day, you may use a bonus action to recover all of your power points. In addition, you may use PP Recovery 2 times per day (still requiring a short rest for each use).
True Manifestation: Select one of your True Powers and two of your Major Powers. You may manifest these powers once at no power point cost. You must complete a short or long rest before regaining the use of True Manifestation.
Innate Mental Powers:
Telepathy:
Sense Emotions
Range: 30 feet
Duration: Concentration, up to 10 minutes
You can sense the emotional state of a visible target. Alternatively, you can sense the emotional state of a group of people within range. Because of your knowledge of true emotional states, you gain advantage and expertise in skills related to social interactions with the target(s).
Short Range Mindspeak
Range: 30 feet
Duration: 1 minute
By manifesting this ability, you can speak with any sentient creation within range by telepathy. Differences in languages does not limit your ability to communicate. If you or the subject move beyond the range, this power ends.
Mental Thrust
Range: 60 feet
You attack a foe using the potency of your mind. This power only affects targets that have a mind (including incorporeal sentient undead). The target suffers 1d6 damage and is confused until the start of your next turn. A Wisdom save negates the confusion.
As you level, the potency of this power increases.
Psychometabolism:
Resistance
As resistance
Camouflage
Range: Touch
Duration: Concentration, up to 1 hour
You blend in with your natural surroundings. This gives you expertise on all Stealth or Nature rolls to remain unseen. You may move at your normal movement rate and still retain the benefits of this power. Running (or the Dash action) automatically negates this power's effect.
Body Weaponry
Range: Self
Duration: Concentration, up to 1 minute
You grow powerful claws, which allow you to attack foes in melee combat. You are automatically proficient with the claws. Your damage is 1d6 plus either your strength or your dexterity modifier (you choose).
As you level, the potency of this power increases.
Psychoportation:
Step
Range: Self (30 feet)
You instantly teleport to a spot within range that you can see. If the exit point is near a hostile target, you gain advantage on your first attack against that target, and the target suffers disadvantage on its next action.
Blurred Edge
Range: Self
Duration: Concentration, up to 10 minutes
You are indistinct and difficult to target. For the duration, melee attacks against you (excluding area of effect melee attacks) suffer a 1d4 penalty.
Molecular Dispersion
Range: 120 feet
You teleport molecules from the target, resulting in physical damage. Damage is 1d8.
As you level, the potency of this power increases.
Psychokinesis:
Deflection
Range: Touch
Duration: Concentration, up to 8 hours
The subject of this power gains an armor class bonus of your Wisdom modifier.
Force Hand
As Mage Hand
Energy Ray
Range: 150 feet
You choose a damage type. You fire a ray of the chosen damage type. You deal 1d8 points of damage.
As you level, the potency of this power increases.
Clairsentience:
Enhanced Senses
Range: Self
Duration: Concentration, up to 10 minutes
You gain advantage on Perception roll (and proficiency in Perception if you do not already have it).
Alertness
Range: Self
Duration: Concentration, up to 1 minutes
You gain a bonus to your initiative rolls equal to your Wisdom modifier. In addition, you cannot be surprised and all reaction attacks against you are disadvantaged.
Future Dissonance
Range: 120 feet
You pull future knowledge of the target into the presence, which disrupts their psyche. You deal 1d8 damage.
As you level, the potency of this power increases.
Metacreation:
Trinket
Range: 30 feet
Duration: Concentration, up to 10 minutes
You create a minor object of common materials with no moving parts. The created object can be no larger than a chair.
Mending
As Mending
Ectoplasmic Bolt
Range: 150 feet
You fire an ectoplasmic bolt (force-effect) for 1d8 damage.
As you level, the potency of this power increases.
Powers:
Telepathy:
Minor: Mindlink, Alter Emotions, Read Thoughts, etc.
Major: Imposed Reality, Psionic Blast, etc.
True: Ultrablast
Psychometabolism:
Minor: Alter Self, Cell Adjustment, Enhanced Ability, etc.
Major: Metamorphosis, Regeneration, etc.
True: Infusion
Psychoportation:
Minor: Dimension Door, Blink, Haste, etc.
Major: Teleport, Plane Shift, etc.
True: Demi-plane
Psychokinesis:
Minor: Telekinesis, Molecular Manipulation, Animation, etc.
Major: Kinetic Control, Telekinetic Wall, etc.
True: Disintegration
Clairsentience:
Minor: Danger Sense, Safe Travel, Object Reading, etc.
Major: Clairvoyance / Clairaudience, See the Past, etc.
True: Glimpse the Future
Metacreation:
Minor: Astral Construct, Fabricate, Armor, etc.
Major: Enhanced Construct, Major Creation, etc.
True: Greater Construct