Hi, I have a very specific problem that I seem to can't solve. I am working on a subclass for Warrior. This subclass allows the warrior to cast some spells and I have worked out that it is hardcoded to the Eldritch Knight chart. The problem is that I gave the subclass -at level 4- the spellcasting ability with an ''Additional Spell List'', and at level 5, if a specific feature is chosen (Prerequisite), I want to add more spells to the general pool of available spells. How can I do this? If this is not possible, then I have a second question. Is there a way to add spells to the character sheet without filling up those precious ''0/2 cantrip''s or ''0/4 known''s?

You can find answers to all of your questions in the Homebrew Subclasses & Species FAQ #s 7, 14, and 15: (https://www.dndbeyond.com/forums/dungeons-dragons-discussion/homebrew-house-rules/131411-a-homebrewers-how-to-faq).

#7 includes detailed instructions on adding Spellcasting to a fighter subclass, and the HTML for the Spellcasting table that goes with it.

#14 includes detailed instructions on how to add additional “spells known” to your subclass without taking up those precious known spell allotments.
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#15 includes additional instructions on how to offer them a choice of spells a few different ways, depending on how you want to do it.

If you need further help, please don’t hesitate to ask, either here or in the thread attached to that FAQ.

Even though I've checked your FAQs before I apparently missed those parts. The problem is fixed now so thank you a lot ^^. Also, I thank you so much for the quick response <3

Happy to help. Don’t worry, it’s a big FAQ, even I have to double check what all’s in there from time to time. If you really want to thank me, please vote Very Helpful in the poll attached to that FAQ!