Hey! Do u know any fic in which Steve is a serial killer and Tony is a detective trying to find him, like this “game” of the cat and the mouse? And Tony does not know is Steve the killer but Steve does know Tony is the detective behind his search? (Sorry for my bad English)

There are several Serial Killer Steve/Detective Tony fics.  Not sure they exactly fit your ask, but here you go!

even death by starkravingcap: “You should turn on your lights,” Steve advises him, as
though there isn’t fire and need bubbling under his skin, “You’re
beautiful when they catch your eyes.”Tony is standing in front of Steve, between the couch and the beat up coffee table, in the ‘v’ formed by his legs. “You
don’t like the light,” Tony reminds him, and he reaches out to touch
Steve’s face. His skin is warm and smooth under his palm, “You always
say you work better in the dark.”

I’m Not Trying to Be A Hero by SweetNSimple: “And I wonder, would I give my life/ Could I make that
sacrifice/ If it came down to it/ Could I take the bullet, I would/ Yes,
I would, for you” ~ Keith Urban’s “For You”“So, what?  Brooklyn
Bruiser – modern day superhero and vigilante?”  Stark was highly
skeptical.  And maybe, in the bottom of his heart, a bit jealous.  There
had been no Brooklyn Bruiser in his childhood.But, whatever.  It
was fine now.  Stark had rolled himself out of that particular bed and
there wasn’t enough money in the world to force him back into it. (Tony does computer forensics here… Part of the Morally Ambiguous and Legally Unacceptable series which has a variety of this trope)

Missing and Ravished by SailorChibi:
Officer Tony Stark really did not mean to fall in love with a serial killer.

there are only monsters here by kimmya: He wasn’t ready, not by a long shot, but he
concentrates on the burn of the January cold and the burn of the tobacco
in his lungs and smiles, just a bit. Just an upward twitch on the side
of his mouth, really, not an expression that any passing stranger would
be comforted by. He smiles, and smokes, and waits.

And then some other serial killer fics:

I’ve Lost My Soul (series) by @tari-aldarion:
There’s a List.
And Tony and Steve are working their way through it.

(both are evil)

Drug in Your Veins by Raikishi: He sees Steve break, expression vulnerable for a half
second. It feels better than it should – to know that Steve still can’t
say no to him.Serial Killer!Steve who’s still fiercely protective over Tony and always will be.

Hiding Mask by MystikSpiral: Tony,Miss me? It’s been a while – you know how
things are. Gotta keep em guessing. How’ve you been? You looked
exhausted yesterday, I wanted to do nothing but make you pliant
underneath my fingertips and tongue. You’d like that, wouldn’t you? I
would. Just imagining how your skin would feel against mine is enough to
drive me insane. Even as I write this, my body feels like it’s on fire;
the way I’d hopefully make you feel when I finally get a chance to
touch you.

Do As the Good Day Demands (the Different Man Remix) by samalander:
Steve Rogers can’t believe the world he’s woken up in, but he has an
idea of how he’s going to fix it. And the murders aren’t hard to pull
off, until a certain domestic terrorist waltzes into his life and makes
SHIELD suspicious.

(everyone is evil, mwahahahaha!)