Fiendology

Rather than power granted solely by a patron, your studies of the lower planes and their denizens (and possibly a few deals with beings of power) have coalesced in the ability to temporarily summon fiends and bend them to your will. 

Imp Horde

Starting at 1st level, if you dealt damage with your action, you can use your bonus action to summon 2 imps to your horde. When you do this, the imps in your horde shoot fire bolts,  each doing 1d4 fire damage. At the end of each of your turns after the first summon, roll 1d4. The result of this is the amount of imps that will expire, reducing to ash and returning their essence to the hells. 

The imps follow you and do not take up their own space.

At 6th level, you summon 3 imps instead of 2. 

For example, you deal damage with eldritch blast with your action. You then use your bonus action to summon two imps. these two imps then deal 2d4 fire damage. Since it is the first turn of summoning, you will not roll for imp expiration.

On your next turn, after dealing damage with your action, you then use your bonus again to summon two more imps. This time, you will roll 4d4 fire damage, as you now have 4 imps in your horde. From this turn and on subsequent turns, you will roll 1d4 at the end of your turn to determine how many imps expire. In this example, you roll a 1, and now have 3 imps total at the start of your next turn. 

Fiendish Knowledge

Starting at 6th level, your extensive research of the lower planes has granted you the ability to detect fiends within 100ft of you. On a successful DC13 intelligence check, you can spend 10 minutes studying prints, marks, and signs around you to determine what creature(s) you have detected, all of its damage vulnerabilities, damage resistances, damage immunities, and condition immunities.

Grimoire of Servitude

Starting at 10th level, you have learned to write a magical book that contains the true names of some fiends, granting you dominion over them. As a ritual, you may summon a fiend from the list below, as well as any fiend that you have learned the true name of. This fiend will follow you and fight alongside you and your allies, as if an ally itself. As an action, you may temporarily dismiss the fiend, to be called forth again at the cost of another action. This summoning will last until you take a long rest, where you will need to complete another ritual of summoning to summon the same fiend or a different fiend. 

When you gain this ability, you may summon one of the following creatures-

Barbed Devil

Barlgura

Tanarukk

Shadow Demon

 

 

Summon Fiend Lord

Starting at 14th level, your dominion over the lower planes has grown to the point of near full control. You have learned to twist the Hells and Abyss together, coalescing in one vile being- the Fiend Lord. 

As an action, you may cut open a portal in the fabric of the realm to summon a Fiend Lord. This summoning lasts for 30 seconds (5 rounds of combat). When the Fiend Lord is summoned, all currently summoned fiends deal an extra 1d6 damage on each of their attacks, including the Fiend Lord, Your Grimoire of Servitude summon, and all imps currently in the Imp Horde. This bonus does not apply to creatures summoned after the Fiend Lord has been summoned. 

 

https://www.dndbeyond.com/monsters/4216743-fiend-lord 

Additional Invocations

Imp-plosion

Prerequisite- Fiendology Warlock

As an action, you can send all your imps currently in your horde towards a target where they explode for 1d8 each. This causes all imps currently in the horde to expire. 

 

Devil in the Details

Prerequisite- Fiendology Warlock

You gain proficiency in Investigation, History, and Arcana.

 

Fiendish Resistance

Prerequisite- Fiendology Warlock, level 10

Once per short rest, you can spend a reaction to gain the resistances of your summoned fiends for one minute. 

 

Blood Pact-

Prerequisite- Fiendology Warlock

Once per short rest when you take damage, you can instead have one of your summoned fiends take the damage for you.