Long story short I informed the owner of the gas station that (after many attempts) the manager would not pay me my winnings from a pull tab game at the station. The manager and I then had an exchange of words (no physical threats) and was told to leave and is no longer welcome there. I have gone in since then and the owner served me no problems and never said anything about me not being allowed in. I went back in today and the manager again told me to leave and would not serve me. I'm from Ohio,USA. My question is, does the gas station have to file anything to keep me from coming in, trespassing list, or is the manager just on her high horse?
A property owner can tell you that you are not permitted on the property at any time; they can change their minds as often as they want; and they do not have to file paperwork or go through any process for that order to "take effect". A manager who is not the property owner can do likewise, acting as an agent for the property owner. Then, if they tell you to leave but you don't leave they can call the police, who can arrest you for trespassing.
One generally has a privilege to be in a public place of business, but not in a stranger's house. Being on someone's property without a privilege to do so is against Ohio law. So you cannot just wander into a residence, but you can wander into a public business, up to the point that there is some notice that you can't go there (e.g. employees-only sign, no entrance etc). This includes a verbal order to leave: when they tell you to leave, you have no privilege to remain, and now you are in violation of the law. Per your description, they have not been entirely clear on whether you lack the ordinary privilege that others would have as customers. They might call the police who might arrest you for trespassing, but you might be able to defend yourself against criminal charges on the grounds that it is not clear beyond reasonable doubt that you lack the privilege to be there. Especially since the owner and manager have different policies, there is reasonable doubt that you have committed a crime.
The relevant law is § 2911.21 of the Ohio Revised Code (ORC).
(A) No person, without privilege to do so, shall do any of the following:
(1) Knowingly enter or remain on the land or premises of another;
(2) Knowingly enter or remain on the land or premises of another, the use of which is lawfully restricted to certain persons, purposes, modes, or hours, when the offender knows the offender is in violation of any such restriction or is reckless in that regard;
(3) Recklessly enter or remain on the land or premises of another, as to which notice against unauthorized access or presence is given by actual communication to the offender, or in a manner prescribed by law, or by posting in a manner reasonably calculated to come to the attention of potential intruders, or by fencing or other enclosure manifestly designed to restrict access;
(4) Being on the land or premises of another, negligently fail or refuse to leave upon being notified by signage posted in a conspicuous place or otherwise being notified to do so by the owner or occupant, or the agent or servant of either.
Let's restate the facts of our hypothetical simpler:
Bob did get into a fight with Adam. It is not relevant what the fight was about. As a result, Bob was informed by Adam, who's agent of the owner Charlie, that they are no longer allowed on the property and that there will be no contracts (=sales) with him anymore with words that amount to "Leave, you are no longer welcome here."
Onto the analysis
The Gas station is a private property of Charly and is open to customers during the opening hours. Outside the opening hours, nobody but the owner and their agents is allowed there.
However, Bob can no longer be or become a customer, as the owner's agent used the delegated freedom to contract of the owner to stop any future sales to Bob. As a result, Bob is not part of the group to which "the use of [the property] is lawfully restricted to certain persons [e.g. customers]". Bob was informed of this, so he is knowingly entering the premises while not part of the group that is allowed there. So he is Trespassing under ORC $ 2911.21(2).
It gets a little complicated as Adam either didn't inform Charly or didn't do so in a clear enough manner, that they put Bob on the no-serve list. However, that doesn't change that Bob was knowingly entering the premises after Bob was told they were banned. The words of Adam that amounted to "Leave, I will not serve you" did either affirm the ban or reinstate it, should Charly have lifted it in the meantime. As a result, Adam is fully entitled to enforce the ban by calling the police, should Bob not leave.
Charly is allowed to lift the ban and allow Bob on the premises and as a customer again at any time, or to instruct Adam to do so, but Bob is not entitled to this. On the counter, Charly is also allowed to reinstate the ban at any moment, if it is just clearly communicated to Bob. It is up only to the discretion of Charly. As Charly's agent, Adam can do so just as much, unless he is specifically instructed by Charly not to.
The reason for the argument is an entirely separate claim and can be brought in small claims court against the business of Charly, as Adam was only acting as an agent in the argument.
does the gas station have to file anything to keep me from coming in, trespassing list?
No. The gas station, through its authorized agents, may exclude you from its property and deny you service in its sole discretion, without legal process, for a non-discriminatory reason, and the reason in your case is not an illegal or discriminatory reason.
If you disregard their instructions, you can be prosecuted criminally (or in a civil lawsuit for money damages) for trespassing without prior legal process.