Will the jail time I served go to my record? Will it affect my filing for citizenship?

Only arrests and convictions appear on a criminal record.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. A lot depends on what you were charged with and what crime you were convicted of or plead to. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your case. He/she would then be in a better position to analyze your case and advise you of your options.

The conviction is what goes on you record and that is what affects citizenship. This is if it is one of the type of convictions that count according to USCIS.

You are really asking two questions. First, it's not the jail, but the conviction that affects your status. Typically, a DUI that carries a potential penalty of less than a year in jail is not going to bar you, but all naturalization applications require 5 continuous years of no violations, so you may have to wait. Secondly, this is an example of why you need to speak with a qualified immigration lawyer before entering into any criminal plea bargain.

Generally if you served jail time in fraction will go on your record. Depending on what the impression is in your immigration status it may well have an effect on your ability to gain citizenship or continuing US residence. I would suggest you seek counsel.