Predestination what does the Bible say and Rev 13:16 about *small* and great..does it mean *small* children..?

Predestination and Psalm 69:28 NASB & CSB say “may they be erased (CSB) or ‘wiped out” (NASB). Most other translations say “Blotted out” (LSB/NKJV) “from the “book of life” (CSB & NASB) most other translations say: “book of the living.” This verse sometimes interpreted to oppose “once saved always saved, and even predestination.” Which book is being referred to? Is it the book of Divine predestination or is it some kind of book like a church membership register of believers in Jerusalem are some of the questions by you that we're delving into this week