will an underage citation go on my back round check if it happened INDOORS ON PRIVATE PROPERTY

I am not sure why you put indoors and private property in all caps.  Those arent issues that have any bearing on your question.  The simple question was were you in possession or consumption of an intoxicating beverage at the time the officer encountered you.  There may be suppression issues as to how he got into a position to observe you but you have been charged with a crime.  If you were found guilty of that crime then it will be on your background check.  The fact that the charges are pending may also be on your rap sheet.  If you haven't been found guilty you should consider challenging the charges.  There are plenty of diversion programs that will leave you without a conviction and again you may have a suppression issue as to the officers observations.  A local defense attorney can walk you through the particulars.