H1B transfer from one employer to another

I am currently working on F1 visa in the US and my H1 petition got approved for FY 2017. I wanted to know how soon can I change employers after Oct 1st? Is it a requirement that I need to provide a minimum number of paystubs while on H1 status? Needless to say I have current paystubs of several months but my status is F1.

There is no minimum time that you need to spent with current H-1 employer. You can move out as early as Oct 1st week. If you move out after Oct 15, or Oct 31, then you would need 1-2 H-1 payslips to cover that Oct H-1 period.