What is incumbent upon one who intermingled the intention for a fard (obligatory) prayer with the intention for the sunnah (supererogatory) prayer preceding it, and sometimes performed the fard prayer after intending for the sunnah and then the fard, and sometimes insisted on intending directly for the fard, and this continued for three months?

You are afflicted with waswasah (obsessive whispering), and it is obligatory upon you to disregard it and continue with your prayer. So, if you intend an obligatory prayer and then waswasah comes to you suggesting that you are praying a supererogatory prayer, do not pay attention to it and proceed with your prayer. However, if you interrupt the intention for the obligatory prayer and intend a supererogatory prayer during the salat, or you become certain that you did not intend the obligatory prayer from the beginning, then your prayer is not valid as an obligatory prayer. But if you are not certain, then proceed with your prayer and disregard the waswasah. You must make up the prayers that you are certain you invalidated or did not intend as obligatory from their inception. As for what you merely doubt, you are not required to make it up.