Some people say not to cut your nails, or trim your hair and beard on Tuesdays. Is there any hadith or verse in support of this, or is it just a superstition?
Your profile says that you are from India and this is an Indian tradition followed by Hindus for ages.
Let me assure you that there is no day that Islam considers inauspicious for cutting nails or trimming hair. This tradition has penetrated into Indian Muslims through Hinduism.
According to what I know and what I have heard about this tradition is that the Hindus consider this day auspicious.
Tuesday = (मंगलवार) Mangalvaar.
(मंगल)Mangal = very auspicious.
On the auspicious day of Mangal (Also the name of Hindu God of war who is very hard to please), they avoid all kinds of nonconstructive works. Cutting nails, trimming hair and shaping beard are just a few to name them.