Are monkeys clean pets to have them inside?

No.

Monkeys make terrible pets.

They're very difficult to housetrain(that's why you often see them wearing diapers). Monkeys are very active and need to be kept occupied to remain physically and mentally healthy. Monkey diet is also very important.

Many have very special nutritional requirements that has to be met to keep them healthy.

They're also quite long lived, so you're stuck with the responsibility for a very long time.

Do the clever thing and settle for a less unusual, but more easily-kept pet. It'll make you all happier. If you like monkeys that much, spend the money on a year pass to the local zoo instead.