Is writing a sign saying "Please turn off your mobile phone before entering the mosque" on the mosque door a form of violence and prohibited, knowing that it has reduced phone ringing during prayer?

What you did is a good deed for which you will be rewarded, because it alerts worshipers to the necessity of turning off mobile phones upon entering the mosque, lest it disturb those praying. This is an alert to a good deed and an act of obedience to Allah Almighty. The Prophet, peace and blessings be upon him, said: "Whoever points to a good deed will have a reward like that of the one who does it."