No.
Here's the list of supported cpus for your board:
https://www.asrock.com/MB/Intel/B250M Pro4/index.asp#CPU
On that site only single board meets your requirements ( <=$65).
https://www.computeruniverse.net/en/c/hardware-components/motherboards?refinementList[facets.Chipsatz.values][0]=Intel B365
I'd suggest you upgrade your budget to at least $85.
https://www.computeruniverse.net/en/asrock-b365m-pro4
The 9100f is locked and lacks any integrated graphics.Ok, what about H310 and B360 cheapsets? This processor is locked for overclocking, isn't it?