Is it permissible for someone who doubts the number of rak'ahs of Witr prayer to build upon the lesser amount, and what should they do if they remember after the tasleem that they prayed three rak'ahs?

The fundamental principle is that whoever doubts the number of rak'ahs should build upon the minimum certain number, due to the Prophet's (PBUH) saying: "If one of you doubts in his prayer, and he does not know how many he has prayed—three or four—then he should cast away the doubt and build upon what is certain, then prostrate twice before giving the salutation." This ruling applies to both obligatory and supererogatory prayers. However, if doubt is persistent for someone, then they should disregard it and build upon the larger number; even if they build upon the lesser number, their prayer is not invalidated.

If the worshipper builds upon the minimum and then it becomes clear to him that he inadvertently added an extra rak'ah, and he remembers this soon after, he should perform the prostration of forgetfulness (sujud al-sahw). If he remembers after a long time, nothing is required of him. The evidence also indicates that if someone adds a rak'ah to their prayer forgetfully, their prayer is valid, and they should perform the prostration of forgetfulness if they remember soon after the salam. If a long time has passed, then they do not prostrate.