So far the petcock doesn't show signs of external leakage? The bike was running fine until you turned the valve.. This seems to indicate the rubber seal inside had rotted away and finally broke into pieces when the valve moved.. a piece is now blocking flow.
Depending on it's construction details the petcock might be difficult to work on. Dis/reassembly without removing the petcock from the tank is tricky. And in this case there's still fuel in the tank.. if this fuel isn't somehow drained beforehand it's gonna start pouring out as you loosen things.
There's usually a strong spring that maintains petcock sealing pressure. A couple of parts need be held in position against the spring pressure while it's small cover screws are reinserted.. The last time i messed with one i was thankful for having least two good hands.. more woulda been better..
That valve sounds like a candidate for replacement. It is likely fastened onto the tank by a double-nut with both left and right hand threads. This allows you to tighten the petcock while positioning it's lever conveniently outwards. If this is understood the removal and replacement of the entire unit is not too challenging.
I've never priced such work and have no idea about cost. A competent mechanic in some small engine repair shop should be able to replace it in a few minutes..