These are like False Gods - you will encounter them when you hit fight False God button.
However, these Gods are "Unorthodox" because each has a different catch than a normal False God. For example, starting with a prestart pool of quanta, having pets out on the field, or using unupped cards vital to strategy.
Possible ones:
Light's Princess - Uses unupped FFQ's. Starts with 2x untargetable Marks of Air in addition to her 3x Marks of Life.
Weapon Master - Has an extra weapon slot. Frozen Voodoo dolls will freeze both weapons.
Master Hand - Randomly delays an enemy creature for 2 turns every now and then.
Lucky 7's - Draws as many cards as he wants (max 7).
Insanity - Mark switches each turn.
To all of you who are going to say "This was already done! Here's the link!", NOTE THAT I WAS REDIRECTED TWICE ALREADY. So don't.