Do you need genuine fuel cap? ?

Check the trouble codes with a scanner first.  Do not waste your money on a new cap, genuine or not.

Yes.           

Why no, no you don't.

I never had that problem using a Stant brand gas caps on my Toyotas. Before you assume other parts may need replacing, you need to have the OBD2 trouble codes pulled at a car part store for free. Look up the definition of each code for what it means. No codes tell you to replace a part, but the do tell you which parts and systems need to be tested to determine corrective measures. OBD2 does not guess, it is exact.

1st shut off the engine. Remove cap & put on for sure properly. Restart. If light goes out= Done.

Only if you have a Toyota.

Just examine the existing fuel cap rubber seal for cracks.

If it's still flexible and shows no cracks, it's probably not bad and you may have a leak elsewhere.

Odds are it is not the cap, so try the one you have on hand for now.

If you have a P0442 cod for a small evap leak it could be the gas cap causing the leak BUT there are other things that can also set that code. If you put a cheap after market gas cap on the vehicle and the code comes back you won't know if the cheap gas cap is sealing or not or if you have another issue. I'd buy the stock gas cap if not testing the gas cap with a Miller vacuum tester.

Ask the engine why the light is on first. P0455 or P0457 indicate a leak in the evaporation emissions system or a loose gas cap respectively. If that's the case, the gas cap is a good bet.