Is a prayer considered to have been performed on time if the worshiper started it 3-10 minutes before its time expired and completed it after its time had expired, or is that considered to be outside its time and a major sin?

Whoever catches one rak'ah of the prayer before its time expires has caught the prayer as adaa' (performance within its prescribed time) and not qadaa' (performance after its prescribed time). This is based on the saying of the Prophet (peace be upon him): "Whoever catches one rak'ah of the Fajr prayer before the sun rises, has caught Fajr; and whoever catches one rak'ah of the Asr prayer before the sun sets, has caught Asr."

As for whoever catches less than one rak'ah, scholars have differed regarding its validity. Some held that it is not caught, while others held that it is caught by catching a part of it, such as the ihram (opening takbir) or a prostration, citing as evidence hadiths such as: "Whoever catches one prostration of the Asr prayer before the sun sets, let him complete his prayer."

A Muslim must maintain prayer within its prescribed time, and delaying it without a valid excuse is among the grave sins, based on the words of Allah the Almighty: "Indeed, prayer has been decreed upon the believers a book [to be observed at] fixed times," and "So woe to those who pray, [but] who are heedless of their prayer."