What is the ruling of Islamic law regarding feeling as if a release of wind has occurred during prayer, when it has not actually occurred, and does this invalidate the prayer, or must it be repeated?

Prayer is not invalidated simply by holding back wind or feeling the need to expel it.

If the desire to expel wind occurs before prayer, it is better to relieve oneself and perform ablution for prayer with presence and devotion.

If the urge to expel wind arises during prayer, there is no harm in completing it, nor is it disliked, and the prayer is valid.

It is not permissible to begin prayer while suppressing the two impurities (urine or feces), due to the Prophet's (peace and blessings be upon him) saying: "There is no prayer in the presence of food, nor while one is suppressing the two impurities." However, the prayer of one who prays while suppressing them is valid but incomplete.