Possibly, and the fact that you are the child's parent rather than a random person with a felony record is your strongest argument for getting approved.
Most correctional facilities have an automatic restriction on visitors with felony convictions, and Potomac Correctional Center in West Virginia follows standard West Virginia DOC visitation policy which includes that restriction. The standard process does not approve felons for visitation without additional review. That is the baseline you are working against.
However, the parent of an inmate's child occupies a different position than most felony-restricted visitors, and facilities recognize that. The ability of a child to maintain a relationship with an incarcerated parent is considered a legitimate interest, and you are the vehicle through which that relationship can happen. That gives you a genuine and compelling case to make.
The process requires a formal petition to the warden or captain requesting a special waiver to the standard felony visitor restriction. Your petition should be specific and focus on a few key points. You are the mother of the inmate's child. The child deserves the opportunity to maintain a relationship with their father. You are the only available option to facilitate that visit. Your felony conviction is documented and you are not attempting to hide it.
The tone matters. Come in as a cooperative, transparent parent advocating for your child's relationship with their father, not as someone demanding rights you feel are being withheld. That framing gives the warden a reason to say yes.
Call PCC directly, ask who handles special visitation waiver requests, and ask what the formal petition process looks like. Get that process started in writing.