There’s no direct cause and effect between believing in a religion and living a longer, happier life.
However, religious people are more likely to attend regular religious services, where they are likely to develop social connections. As social animals, social connections are great for our physical and mental well being. This is probably one of the factors that leads to religious people living longer, happier lives (Association of Religious Service Attendance With Mortality Among Women https://jamanetwork.com/journals/jamainternalmedicine/fullar...)
You got the citation you wanted?