Our lives, as Christians, are shaped by our God who is three persons. It has effects on every aspect of who we are and how we are to live. And it should definitely impact our prayers. Both how we pray and what we pray should be shaped by each person of the Trinity.
"For this reason I bow my knees before the Father, from whom every family in heaven and on earth is named, that according to the riches of his glory he may grant you to be strengthened with power through his Spirit in your inner being, so that Christ may dwell in your hearts through faith." Ephesians 3:14-17