Where did columbus believe he had landed in a new and claim territory off the coast of asia near the american continents on the caribbean islands

He believed he landed in multiple places because he landed in multiple places.

This is a bit more detailed part of where he thought he landed

On August 3, 1492, Columbus set sail from Palos, Spain, with three small ships, the Santa Maria, the Pinta, and the Nina. On October 12, the expedition reached land, probably Watling Island in the Bahamas. Later that month, Columbus sighted Cuba, which he thought was mainland China, and in December the expedition landed on Hispaniola, which Columbus thought might be Japan. He established a small colony there with 39 of his men. The explorer returned to Spain with gold, spices, and “Indian” captives in March 1493 and was received with the highest honors by the Spanish court.

the declaration states, “we hold these truths to be self-evident, that all men are created equal, that they are endowed by their creator with certain unalienable rights, that among these are life, liberty, and the pursuit of happiness….”