I have been doing tayyammum on the roof of my wardrobe because it has dust on it. After I do tayyammum here, there are handprints left - but there are spaces of dust between the handprints and between the fingers on the handprints.Is it permissible to do tayyammum on these smaller areas?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If there is dust on this object that sticks to your hands when you strike it, then it is permissible for you to do Tayammum with it, but if there is no dust on it that sticks to your hands, then you should not do Tayammum with it.

Ibn Qudaamah said: “If a person hit his hands on a rock or a wall or an animal or anything else, and dust stuck to his hands, then it is permissible for him to perform Tayammum with it, but if there is no dust on it (that object), then it is not permissible.” [End of quote]

Allaah Knows best.