To change your father to be your biological father, if that is what you want to do, you would go into edit on your profile. On the right where you see your 'other' father, you can select the 'replace/remove father'. On the next page, enter the wikitree ID of your biological father in the top box, BUT do not select the Go, You need to scroll to the bottom and 'uncheck' the box so that your 'biological father' is not entered as a 'spouse' of your mother, unless, of course, they did marry for a time. Then, select the Add father button.
Your 'biological' father will show as connected to you with his biological family. Your mother will show as connected, but your mother's profile will not show the connection to your 'biological' father.
You can have the information in your biography about your 'other father' using his 'wikitree ID' and name so you or anyone else could easily connect to his profile, ie [[Father ID | Father name]]