Interesting concept! I can't comment too much on the balance, but I still have come criticisms.

• Charisma doesn't make a whole lot of sense for a saving throw proficiency. I would probably replace it with Intelligence.
• The weapon proficiencies are also a bit odd. The player starts with melee weapons, gets access to fighting styles that benefit their usage, but isn't proficient in them? They should at least get proficiency with all simple weapons maybe a list like: "simple weapons, blowgun, hand crossbow, heavy crossbow, longbow" would be good.
• No abilities at second level? I guess that might be because that's when the ranger gets spells and you removed that. It's super disappointing to level up, especially after the first level-up of the game, and get literally no new abilities. Out of all the base classes in the game, only spellcasters get "dead levels" (levels without any features), and that's because they get access to the next spell level on those levels (exception: the warlock's level 18 is dead, but to be fair that's after they can cast 9th level spells, plus they at least get a new Invocation). Maybe give them Action Surge or something?
• The whole class feels very loaded towards the subclasses doing things while the "chassis" of the class doesn't do a whole lot. I'm not sure if that's a bad thing or not, but that definitely stuck out to me.
• I feel like it would make more sense for the Spellshot to be a ⅓-caster (like eldritch knight or arcane trickster instead of getting spells up to 7th level. That's how other subclass casters do it. Subclass casters also usually get their own spell lists.
• Magic Arrows is super confusing, relies too much on randomness, and doesn't scale well.
• I know I'm being mostly negative here, but I really love the concept behind the Jagged Arrow archer. It's a very flavourful concept and I feel like we need more subclasses like that.