What should a person do who leads prayers (imams) for the worshippers in his village, while some of them dislike his imamate claiming he prolongs the prayer, and should he refrain from leading prayers in this case?

The Sunnah is for the most knowledgeable of Allah’s Book among the congregation to lead them in prayer. If you are such, then it is more befitting for you to step forward to lead, and the dislike of some, if unfounded, should not harm you. If you forgo leading in order to reconcile their hearts and prevent discord, there is no sin, provided that the one who leads the people in prayer is proficient in recitation and does not make an error in Al-Fatihah that alters its meaning. You can arrive before the iqama (call to start prayer) and refuse to step forward to lead if you know that your leading would cause discord.