Archfey focus on Power, Influence, and Understanding, the scholars are no different in this aspect. The scholars will specialize in one of the three areas.

Power is a source of energy. The more power you have the more you can accomplish. You are able to save energy and use your spell efficiently.

Influence is like a silver tongue. The more you are able to control others and people around you.

Understanding is the knowledge you seek. You know more secrets of the universe.

Fundamental Power

When a creature rolls a 1 on a saving throw against your spell or ability the save is considered failure and any damage it would take is doubled.

Influence of Fey Tongue

You gain proficiency in Persuasion and Deception

Understanding Nature

Your understanding of the Fey infuses you with the ability to cast certain spells. You learn the druidcraft cantrip and at 2nd, 4th, 6th, 8th, 10th, and 12th level you gain access to natures spells. You write these spells in your spellbook for free. You always have it prepared, and it doesn’t count against the number of spells you can prepare each day. These spells count as wizard spells for you

 

(Note due to DNDBeyond, cant program the spells, you need to add them yourself)
!sb add spellname

Fey Specialization

Starting at 6th level you start to specialize in your area of choice. Choose between Power, Influence, or Understanding.

At 14th level you may choose a secondary study

At 20th level with racial boon you can choose a 3rd specialization.

Influence Specialization

Creatures can’t have advantage on saves of your spells with charmed you cast.

Power Specialization

Whenever you roll a die you may add +1, this does not change the roll but only the results. for example rolling a 1 on a d20 for a magic wand still destroys the wand. This does not change crit chance.

Understanding Specialization

You gain proficiency in History and Arcana, if you have proficiency you gain expertise instead for that skill.

(add this manually)

Fey Expertise

At 10th level you further expand your specialization to become an expert.

Note at level 20 with racial boon you get expert on the second specialization if you don’t choose a third specialization

Influence Expert

When you cast a spell that includes the charmed and one or more creatures are immune, you may inflict the effect of bane on any creatures that failed instead of the original spell for those creatures for the duration still using the original spell for concentration.

Power Expert

When you cast a spell expending a spell slot that targets a single creature and forces them to make a save, if that creature succeeds on the initial save you may regain that spell slot. Once you regain spell slots a number of times equal to your proficiency modifier you can’t use this ability until you complete a long rest.

Understanding Expert

When you make an Intelligence ability check and roll a 9 or lower it becomes 10.

Fey Mastery

At 14th level you choose between Power, Influence, and Understanding a mastery based on the choice you made at 6th level

Influence Mastery

When you cast a spell with charm you may replace charmed with Frightened, Poisoned, or Grappled.

Your spell uses nature to generate a toxin to poison or grasps with vines to grapple.

Power Mastery

When you cast a spell using a spell slot roll a 1d6-2 if the result is higher than the level of the spell it it doesn’t expend that spell slot.

Understanding Expert

When you take a long rest pick one item or one creature you are familiar with. You gain a deep understanding of their abilities, effects (if any) and origins (DM's Discretion). When you make a 1d20 roll for or against the chosen item or creature, you gain advantage and an additional 1d4 to the total. If you subject the chosen object or creature to an effect that requires a roll, the target must roll a 1d4 and subtract it from the roll.