I seriously don't think there is any problem because individually you have done nothing wrong, as you said above. However, in another statement, you mentioned, "I have no criminal case pending against me," which I want you to clarify. Is there anything that you are not comfortable sharing with us? The property dispute/FIR against your family and anything that can affect your career are totally different matters.
Second, you must not take it as if this issue can affect your professional life, or I should say you must not drag these personal things into your professional life consideration. Although, I accept sometimes these kinds of problems bother us a lot and force us to think over these things or put us in a dilemma about whether these can disturb our professional life or not, we often forget in this situation that by taking worries and mixing our personal life problems with our professional life, we are actually allowing them to bother our professional life.
Also, I do not agree with Sharmila Ji that you should tell all about the FIR and dispute to your employer, which can certainly affect your job and create many questions and doubts/inquiries on an immediate basis, and I believe that you won't really accept. However, I accept background verification may disclose these things, but we must not forget these are related to your personal life, not concerning your career life or past employments, which actually matter most for your employers/recruiters.
Moreover, with the process of background verification, recruiters and employers like to know the work history of an employee/candidate, nature and behavior/dealing at work, and any legal/criminal activity (if any) in personal and professional life which can affect them in any way, not about family disputes and issues running in the family. Though these issues and family problems can impact a candidate/employee mentally, if you are strong or are able to handle yourself (i.e., depression) and never let these things come into play at work, there would be no problem for you. Now it's totally up to you.
One thing I really don't understand is why people are scared of background verification and feel like recruiters/employers are very much interested in knowing their personal life or, should I say, consider it more than employment history.
Lastly, I seriously want to know from candidates/members, how many of you have experienced or, being a recruiter/employer, have adopted this kind of background verification in your professional life?
I would suggest you be free-minded and step ahead with confidence in your professional life and must not share these family problems with your employers/recruiters.
For example, a candidate must not share family information or any kind of family details during an interview unless asked by the interviewer, so the same applies here. You must not be too honest but professional, sincere, and confident. Hope you got my point.
Best of Luck