Zardnaar
Legend
I feel like we do have a number of versions of this already:
Valor Bard
Eldritch Knight
Swordmage
Bladelock
I've played all 4 of those - and each felt Gishy from the get go. I walked into melee battle and used a combination of magic and melee to get the job done with each.
Valor Bard - this is perhaps the most obvious blending of magic and might. Eldrtich knight - I played a human variant with a feat to get a spell at level one (and cantrips) - so it was very gishy.
Swordmage - Sword wielding spellcasting elf from level 1 on....
Bladelock - This was a bit less gishy for levels 1 and 2 - but we hit level 3 VERY quickly (I think it took about 10 hours of game play to get there).
None of them are actually that good though and often flawed in some way RAW.
My concept is a half caste rlike paladin with the ability to sacrifice spells for more damage (probably advantage toi hit and less damage than a Paladins smite). Baked in would also be proficiency in con saves, heavy armor and the hand free ability of the warcaster feat.
It would be an arcane paladin more or less with a focus on buffing, damage, and better offensive spells vs smite, healing and aura.
I suppose you can also MC Paladin and Sorcerer together to get something similar (Paladin 6/Sorcerer XYZ takes a while to come online though).