Very interesting, I wonder where this will end up.

I wish we will see All Might offering him OFA and Izuku flipping the bird and tell him to go screw himself with his fucking quirk he don't need it anymore and seeing a angry mama inko yelling at all might cause his poor baby getting shot because of him

"Izuku kept shooting "discreet." worried glanced at Izuku."? Didn't you mean "Inko"? (also, they're "glances", not "glanced" - which I wouldn't have even noticed had I not typed it out myself).

Good start to filling in the background story (you've clearly established where your story branches off from canon). However it isn't complete. You still have to explain how Midoriya became a police detective (especially when he should still be in his third and final year of high school).

Also, it seems like Midoriya made more than one impression on All Might (enough to leave the hero speechless). As such I would have expected his reaction back in the first chapter upon seeing Midoriya (who had just taken a bullet for him) to be one of shocked recognition, although I suppose you could be saving that for a future chapter (perhaps a confession of his mistakes to Tsukauchi, who
fortunately for him probably won't go physically beating him over the head for being so insensitive like Recovery Girl or Midnight probably would).

Poor Izuku

Me want more

interesting I hope he does not inherit the quirk of all might and is more dependent on his own physical strength and I hope he also uses special equipment to complete his mission

Im interested, reallly good :)

I was wondering when someone would make a fanfic with Izuku a detective or an armed prosecutor. I recommend getting references from Hidan no Aria.

Please keep it up!

Sometimes taking a break and writing something else can help. Supposed once when Japanese light novel author Kazuma Kamachi was asked what he did to take a break from writing, responded "Write something else."

I was a little thrown off by Midoriya's appearance when Yagi* at first encounters him on the street however working undercover would explain the worn and torn clothes (*and yes, I'm going to insist on continuing to refer to him by his last name for the moment, since about the only ones who ever seem to call him Toshinori are Tsukauchi, Gran Torino and sometimes Recovery Girl).

In all fairness Yagi's advice to Midoriya was valid, even if it was delivered in arguably the worst way possible. Now that Midoriya has taken that advice (despite it's poor delivery) it will be interesting to see how this story develops. Given that Yagi is still able to perform hero work for up to an hour a day it sounds like he may still searching for a successor, but at this point it would probably be a bit awkward to offer it to Midoriya.

Speaking of names, the Principle's name is "Nezu", not "Nedzu" (that seems to be a common error - one which I've made myself).

This is interesting

Seems interesting, I want to see how everything actually changes and impacts others and especially All Might.