Genesis 5:32 indicates that Noah became the father of Shem, Ham and Japheth from the age of 500 years old, but does not list in detail their specific years. (Noah was 600 years old at the time of the flood in Genesis 7.) An incident involving Ham is related in Genesis 9:20-27.
20And Noah began to be an husbandman, and he planted a vineyard:
21 And he drank of the wine, and was drunken; and he was uncovered within his tent. 22 And Ham, the father of Canaan, saw the nakedness of his father, and told his two brethren without. 23 And Shem and Japheth took a garment, and laid it upon both their shoulders, and went backward, and covered the nakedness of their father; and their faces were backward, and they saw not their father’s nakedness.
24 ¶ And Noah awoke from his wine, and knew what his younger son had done unto him. 25 And he said, Cursed be Canaan; a servant of servants shall he be unto his brethren. 26 And he said, Blessed be the LORD God of Shem; and Canaan shall be his servant.
27 God shall enlarge Japheth, and he shall dwell in the tents of Shem; and Canaan shall be his servant.
—Authorized King James Version