Are blue eye charms or the hand of Fatima permitted in Islam?

No. Wearing or hanging objects believed to repel the evil eye is not permitted, and the ruling is clear.

The Prophet, peace be upon him, stated that whoever hangs an amulet has committed shirk, and instructed that such items be cut off and removed. The problem is not the object itself but the belief attached to it: that a piece of glass or metal can prevent harm that only Allah controls.

This covers blue eye beads, the hand of Fatima, horseshoes, red threads, verses folded into lockets, and taweez written by practitioners.

What to use instead

• Morning and evening adhkar, consistently
• Ayat al-Kursi after each prayer and before sleeping
• The three protective surahs, three times each morning and evening
• Saying masha Allah, tabarak Allah when admiring
• Reciting over your children nightly

The irony is worth noticing. People wear these objects seeking protection while abandoning the protection actually prescribed, which is free, requires no purchase, and does not compromise anyone's tawhid.