What is the criterion for the distance between two mosques when building them, especially if the mosques are close to each other?

There is no specific legal (Shariah) determination for a particular distance between mosques; what is considered is the need. Therefore, it is not permissible to build a mosque next to another mosque unless the area is large and its residents require more than one mosque. Any mosque built to cause harm or for showing off falls under the ruling of a "mosque of harm" (Masjid al-Dirar), and prayer in it is not permissible. It is permissible to build another nearby mosque if the population increases and the current mosque cannot accommodate them, but this should not be a cause for dividing and scattering the congregation.