A subpoena is not an invitation; it is a court order. Your state may permit nail and mail service (every state has its own rules for service), which means personal service may not be necessary. Also service on a member of your household is considered legally service on you, so you cannot claim you have no notice of this. You can be arrested for ignoring a subpoena. I assume you are being asked to be a witness, and most judges do not take kindly to witnesses not coming to their court.
Mr. Sarno is licensed to practice law in NJ and NY. His response here is not legal advice and does not create an attorney/ client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. Mr. Sarno strongly advises the questioner to confer with an attorney in their own state to acquire more information.
First, I recommend you thoroughly read all the language on the subponea as it should carefully explain all your rights. Generally, under Ohio law, one way a subpoena can be properly served "by leaving it at the person's usual place of residence." There are also rules requiring compensation to you for mileage and attendance which is usually included by check with the subpoena. However, in the past, in a few circumstances, I have brought a check with me and given it to the person at their attendance. I cannot tell exactly from your answer the reason you were supoened or why you are unable to, or do not wish to, comply with the subpoena. The reason I raise this issue is that your short question immediately causes me to think of additional questions which are necessary to fully respond to your question. In your situation, depending on the answers, your question may only be able to be answered by a lawyer. I would not recommend posting any further details on this website as it is a public form and you do not receive the benefit of the attorney-client privilege. In some circumstances, a person who has been subpoenaed can file a "motion to quash" the subpoena but you would need to speak to a lawyer about this. In my experience, as a civil lawyer, I have served subpoeans for fact witnesses, with key relevant factual testimony necessary for a jury to hear, to show up in Court and/or provide deposition testimony. Depending on the circumstances, you my want to hire a lawyer to review all of the facts. I can also tell you that people there have been many times in the past I have subpoeaned a person and the person called me and asked to work out a different time and/or come up with an alternative because there was a unique situation that called for the request. For example, the person may have a vacation scheduled or may have had a surgery or medical procedure scheduled or was in the hospital. In those circumstances, I was able to usually work with them to accomadate the unusual need or circumstance. However, I am not recommending that for you as you may first need to consult with a lawyer.