There are various beliefs regarding which son was responsible for the Asian peoples.
This site (http://www.askelm.com/prophecy/p950701.htm ) has a good reference giving the source of Asian peoples as Kittim grandson of Japheth.
Here are the pertinent paragraphs
“Look at these Japhetic peoples for a moment. We know that Meshech and Tubal are associated with Eastern Europe and Central Asia. Some people have even connected the city of Moscow in Russia with Meshech. That is a possibility. These nations of Japheth moved north and then on farther east. Later on, we find that Gomer and Javan and the others of Japheth followed them into the east into the region of what we call China today. They also went into Southeast Asia, and then through the Malay archipelago into various islands of the ocean… Look at what this means in regard to the Chinese who were once known as the people of Cathay or Kittim.
Believe it or not, the Kittim people were the original ones who first settled the island of Cyprus in the eastern Mediterranean after the Tower of Babel incident. From there they went further westward and made settlements in Italy.
Then they were pushed northward and then eastward by Semites coming from the eastern Mediterranean areas. The people of Kittim journeyed even further north and then eastward into the central areas of Asia, and finally winding up in the region we now call China (indeed, an early name of China was Cathay which comes from the root word Khitai which also answers to Kittim, the “im ” is plural).”
Here’s an article giving the sixteen grandsons of Noah and the cultures/countries that descend from them. Also answers two common questions on race and that pesky “did God really condemn interracial” marriage questions.