Can I apply for naturalization after my probation ends?

Why did you plead guilty if accused wrongly? I would need many more facts to adequately advise you along with a certified copy of all court records.

You have to prove good moral character for the 5 years (3 years if married and living with U.S. Citizen) preceding the date you file your N-400 Application. A conviction of a crime involving good moral character, such as larceny, would mean that you have to wait 5 years from the date of the conviction. Whether you were wrongly accused does not matter, what matter is whether you were found guilty. Also, please be aware that many criminal convictions can result in your being deported or removed from the U.S. By filing for Naturalization you would be telling the USCIS of your conviction. Therefore, you should speak to an immigration attorney regarding your situation before you file. Additionally, you should speak to them even if you decide not to file since you could have a problem re-entering the U.S. if you leave because of your conviction.