When the rebels besieged the house of Uthman, the siege was not severe at the early stage. The rebels merely hovered around the house of Uthman, and did not place any restrictions on the movements of Uthman. Uthman went to the Prophet's mosque as usual, and led the prayers. Th' rebels offered prayers under the leadership of Uthman.
"When a person dies, his works end, except for three: ongoing charity, knowledge that is benefited from, and a righteous child who prays for him."
Prophet Mohammed (PBUH)
"The best of what a man leaves behind are three: a righteous child who supplicates for him, ongoing charity the reward of which reaches him, and knowledge that is acted upon after him."
Sunan Ibn Mājah
"Every day two angels come down from Heaven and one of them says, 'O Allah! Compensate every person who spends in Your Cause,' and the other (angel) says, 'O Allah! Destroy every miser.'"
Sahih Bukhari