Is the act of writing beneficial hadiths and phrases on cardboard and distributing them in the mosque considered an ongoing charity (sadaqah jariyah) or beneficial knowledge, and does its reward continue even after it ceases?

Your work of writing and pasting useful phrases on the mosque walls for the benefit of worshippers is charitable and beneficial. We ask Allah to reward you and the mosque's Imam for it. Your purchase of papers and pens is a charity for which you will be rewarded, but it is not an ongoing charity (sadaqah jariyah). An ongoing charity is an endowment (waqf) whose principal is held in perpetuity and whose usufruct is dedicated.