D&D 5E Missing spells school spells at certain spell levels.

[Tales and Chronicles]

there were 3e psychic 'spells' that were basiclt lesser foresight, do they have anything like that?

Yep. As far as I remember, they were intended for a wuxia style of magic where you could deflect arrows and such.

If not, there's always the UA Mystic's Discipline that had a bunch of precognition ''spells'' that could be re-converted from spell points to spell slot and used as-is.

ie:
Mind Storm (5 psi) 3rd level spell, Enchantment. As an action, choose a point you can see within 60 feet of you. Each creature in a 20-foot-radius sphere centered on that point must make a Wisdom saving throw. On a failed save, a target takes 6d8 psychic damage and suffers disadvantage on all saving throws until the end of your next turn. On a successful save, a creature takes half as much damage. You can increase the damage by 1d6 per additional psi point spent on this ability for each spell slot over 3rd level.

Ransack Mind (5 psi; 3rd level, conc., 1 hr.) Divination. While you concentrate on this ability, you probe one creature's mind. The creature must remain within 30 feet of you, and you must be able to see it. If you reach the ability's full duration, the target must make three Intelligence saving throws, and you learn information from it based on the number of saving throws it fails. With one failed saving throw, you learn its key memories from the past 12 hours. With two failed saving throws, you learn its key memories from the past 24 hours. With three failed saving throws, you learn its key memories from the past 48 hours.

Phantom Betrayal (5 psi; conc., 1 min.) Enchantment. As an action, you plant delusional paranoia in a creature's mind. Choose one creature you can see within 60 feet of you. The target must succeed on an Intelligence saving throw, or until your concentration ends, it must target its allies with attacks and other damaging effects. The target can repeat the saving throw at the end of each of its turns, ending the effect on itself on a success. A creature is immune to this ability if it is immune to being charmed.

Tremorsense (1st level conc., 1 min.) Divination. As a bonus action, you gain tremorsense with a radius of 30 feet, which lasts until your concentration ends.

Unwavering Eye (1st level, Divination). As a bonus action, you gain advantage on Wisdom checks for 1 minute.

Piercing Sight (2nd level; conc., 1 min.) Divination. As a bonus action, you gain the ability to see through objects that are up to 1 foot thick within 30 feet of you. This sight lasts until your concentration ends.

Precognitive Hunch (1st level Divination conc., 1 min.). As a bonus action, you open yourself to receive momentary insights that improve your odds of success; until your concentration ends, whenever you make an attack roll, a saving throw, or an ability check, you roll a d4 and add it to the total.

All-Around Sight (2n level Divination). In response to an attack hitting you, you use your reaction to impose disadvantage on that attack roll, possibly causing it to miss.

Danger Sense 3rd level Divination conc., 8 hr.). As an action, you create a psychic model of reality in your mind and set it to show you a few seconds into the future. Until your concentration ends, you can't be surprised, attack rolls against you can't gain advantage, and you gain a +10 bonus to initiative.

Victory Before Battle 5th level Divination). When you roll initiative, you can use this ability to grant yourself and up to five creatures of your choice within 60 feet of you a +10 bonus to initiative.