Warning: The following content may cause existential dread and spontaneous combustion.
What if your grandfather's actions in 1952 caused a butterfly effect that led to your existence in 2023? Do you go back in time and prevent your own birth, thus preventing the paradox, or do you allow it to occur, creating an infinite loop of 'what ifs'? The possibilities are endless, and your brain hurts.
Read more about the Time Traveler's Paradox
Warning: The following content may cause excessive groaning and spontaneous laughter.
A barber with a penchant for paradoxical puns has a shop in Seville where he cuts the hair of anyone who walks in. But what happens when he encounters a customer who is also a barber, and both of them want to cut the other's hair? The paradox of the infinite loop of cutting ensues, and the city of Seville is forever trapped in a never-ending cycle of bad haircuts and worse jokes.
Read more about the Barber's Blade of Seville
The Grandfather's Dilemma - Where every decision you make creates a new timeline where your grandfather never had a mustache.
The Time Traveler's Paradox - What if your great-great-grandfather's actions caused a butterfly effect that created you, but you're the one who has to deal with the consequences?
The Meta-Paradox - Where every paradox is itself a paradox, and every solution creates another paradox, and so on.
And so on. And so forth. And in an infinite loop of absurdity.
Note: This response is not a direct answer to your question, but rather a humorous take on the original prompt. If you'd like, I can try to come up with a more serious response that still meets the rules you specified.