Is it permissible for congregational prayer to be performed in the courtyard adjacent to a mosque or prayer hall, with some people praying in the mosque and others in the courtyard?

It is not permissible to abandon prayer in a mosque designated for it, even if it is small, because it takes the ruling of a mosque and the reward therein is multiplied. This is based on the Almighty's saying: (In houses which Allah has ordered to be raised and that His name be remembered therein; Exalted is He within them in the mornings and the evenings by men..), and based on the saying of Ibn Mas'ud: "Whoever wishes to meet Allah tomorrow as a Muslim, let him observe these prayers wherever the call to them is made."