Is it permissible to go to the mosque to perform the Fajr prayer while the taste and smell of onions remain in the throat after eating them for dinner and then sleeping?

It is disliked for someone who has eaten something with an unpleasant odor, like garlic or onions, to enter the mosque. They are permitted to miss congregational prayer if it is difficult to remove the smell, due to the Prophet (peace and blessings be upon him) forbidding those who have eaten them from approaching the mosques, and because the angels are bothered by what bothers the Children of Adam.

So, if the smell of the onion persists and you cannot find anything to remove it, do not go to the mosque. However, if the smell has gone or you have something to remove it, then use it and go for Fajr prayer. The mere persistence of the onion's taste without any smell does not prevent one from attending the congregation.