I’ve never considered the Arcane Archer to be a fighter and always felt it should be a ranger subclass instead. So I looked at it and realized it is really nerfed. It’s basically an archery fighter with 2 special attacks per short rest - lots of options for those 2 attacks but only 2 Special attacks.

So here is my first try at a Ranger Arcane Archer: 

L3: 1. Arcane shot as the fighter version but proficiency bonus times per rest. 
2. clairvoyance as a spell like ability Proficiency Bonus times/rest.
3. Spells (don’t count against spells known as always):
Level 1) Hail of Thorns
Level 2) Melf’s Acid Arrow;
Level 3) Energy Arrows (flame arrows but you get to choose the energy type: fire/cold/lightning/acid/thunder)
Level 4) Arcane Eye ( I couldn’t find an archery based L4 spell but an archer should always be able to see their targets clearly and this helps that)
Level 5) Swift Quiver.

L7: Misty Step Proficiency Bonus times / Long rest

L11: 1) Arcane Archer improvements as the fighter class
2) You are now able to fire an additional arrow shot as a bonus action (giving you a total of 3 arrows each turn as compared to a fighter’s 3 arrows due to 3 attacks).

L15: you gain the Skulker feat (hide when lightly obscured, misses don’t reveal position when firing from hiding, no disadvantage to perception in dim light).

 Any thoughts/comments/suggestions?

Maybe some way to dispel or counter magic affects that is not counterspell or dispel magic

Maybe add a dispelling shot to the archer options from the fighter