It's a myth.
The Round Earth concept dates back thousands of years ... it was known in the time of the Ancient Greeks.
The Greek historian Herodotus wrote about a voyage by an Egyptian fleet of ships which happened around 600 BC..... around 150 years before his own time.
The fleet sailed south down the Red Sea and followed the coast of Africa - all the way to the southern tip (The Cape of Good Hope)
Then west and north, until they came around to re-enter the Mediterranean at the Straits of Gibraltar.
They reported that when they were in the southern part of their journey the Sun was in the northern part of the sky.....many people, including Herodotus, did not believe them.
So... at that time the roundness was not understood.
But a hundred years later Aristotle was suggesting the roundness of the Earth.
The first person to measure the size of the Earth was Eratosthenes
So .... Columbus?
He simply used a size of the Earth that was more inaccurate than Eratosthenes had found.
He thought it was not very far to India, Japan and China if he sailed across the Atlantic.
This map gives an idea of how Columbus saw the situation.
If the 'New World' had not been there, his sailors would have starved.