What is the ruling on a sum of 50 riyals found outside the mosque: should it be handed over to the mosque administration, does it fall under what people of average means would not bother to pursue so it can be owned, or should it be returned to its place, and is it permissible to leave it and not pick it up to avoid having to publicize it?

A small lost item (Luqatah Yaseerah) that the owner is not keen to find, it is permissible for the one who finds it to benefit from it, and they are not obliged to announce it, as narrated from the Companions. The definition of "small" (Yaseer) is referred to the local custom and common practice of people in that place. Therefore, it is not possible to definitively state that 50 riyals is a small amount without knowing the local custom. If the mosque community is accustomed to dealing with lost items, there is no harm in giving it to them for announcement.