Glad to see someone finally post some new blood in the Fan Fiction category! And, considering we're still in our infancy of the newest incarnation of LupintheThird.net, I welcome you.
Anyway, on to the fic. I really like the idea of Zenigata having a son who, while not wishing to repeat Koichi's mistakes, has a leaning towards police work, and how you specifically set it in Japan (which a lot of people tend to overlook); I was happier still when you mentioned Tokyo Metro specifically. I'm a detail oriented writer. ^^;
Moving on, the short blurb that you posted is alright in general, but there's a few things you should take heed of.
A little more mood setting would be like. For example, what's it like in his apartment? Yeah, the western idea is that japanese apartments are minimalist, but everyone knows that. Does it have a good view? Is there a funny smell? Bad neighbors? Stuff like that.
It's pretty clear Yasuo's got a level of minor depresion going on. No girlfriend, questionable job, more questionable parents, but what else is going on in his life? Why police work? Was it pressure from Zenigata the elder, or did he really want to do it?
Also, what exactly is The Zenigata Curse? You make it sound like obsessive policing, but is that all there is to it?
Again, there's not a whole lot wrong with it, there just needs to be OF it. Definitely a valiant first effort, and you've got spelling and grammar down, which is a definite plus in the world of fanfics. One very minor thing: Change the font and spacing of your fic. Comic Sans is a butt-ugly font no matter what you're using it for, and the big block of text looks a little oogy. Otherwise, keep it coming.
One last note: I liked the idea of starting things off with the Zenigata descendant rather than Lupin/Lupin IV. Take your time in building to Lupin, the build up will make the final appearance of him/him just buggering fantastic.
