(I don't own the rights to any of these characters I'm just a fan making a story, I will be using characters and things from other comic book franchise like Marvel comics, Image comics, WildStorm Comics and The Boys as well as I may use the names of characters, backstories and things within this story)
Earth 3: Batman's Origins
Timothy Fox was the eldest son of three, born into a family of wealth and prestige, his father Lucius Fox was brilliant business manager and corporate executive at Wayne Enterprises as well as a genius scientist and inventor. When Timothy was eight years old, he fell into a cave while playing with his twin brother Lucas 'Luke' Fox, their best friend Bruce Thomas Wayne at the Wayne Manor, which was where he encountered a swarm of bats.
However Timothy was saved by Bruce's father Thomas Wayne the CEO of Wayne Enterprises and a close friend of Lucius Fox, Thomas told Timothy that it is okay to be scared but as long as he doesn't allow fear to control him and those words stay with Timothy even after Thomas and his wife Martha were murdered. Timothy seemingly had inherited his father's natural intellect just like his brother where they both graduated MIT with double degrees in engineering and business management and they soon had hundreds of job offers from around the world, even one from Wayne Enterprises.
However much to the shock of his father and brother Timothy turned down these offers and instead choosing to enter the military, after two tours of duty with the United States Marine Corps, Timothy came home to return to civilian life and to reconnect with his family. Sadly however due to his father's hectic schedule it made any reconciliation between the two difficult, though both continued to try.
During which Timothy saw what Lucius was working in secret on an special suit of high-tech, flight-capable, weapons-equipped suit of powered armor, however Timothy did noticed that something was bothering Lucius so Timothy try to find out what but Lucius refused to tell him which made Timothy even more curious and worry as he saw fear in his fathers eye's. On the night when they going to have a nice family dinner Lucius didn't come home which made everyone worry as they knew how dangerous Gotham City is especially at night, it was past mid-night they revived at a knock on the door and when they open it they saw that it was two police officers who inform the family that Lucius had been murdered.
The news devastated the Fox family however also made Timothy anger and made him wonder that this wasn't just a random murder but was instead it was link to what was bothering his father, so driven to help bring in the ones responsible for his father's murder to justice Timothy returned to the vault where Lucius kept the suit and began to modified it, first by making the suit black, then he added a belt yellow, add pointy ears and add a yellow bat symbol on his chest, the reason why Timothy was adding the bat symbol on the suit was because Timothy fears bats ever since he encountered the swarm of bats when he was eight years old and he was going to those who are responsible for his father's murder fear them as well and and so Timothy Fox became the 'Batman' of Gotham City.
In DC comics there was a event known as Future State where Timothy Fox became the new Batman however I thought why not on a different Earth he didn't just take up the mantle of the Dark Knight instead he was the one who created it