You mean how the child of an immigrant is President?
The president's father was never an immigrant. An immigrant is someone who comes to life permanently in a new country. He was a foreign student with a wife in Kenya and eventually returned to Kenya with an American third wife upon the completion of his studies.
Several presidents have been a child of an immigrant: Thomas Jefferson, Andrew Jackson, James Buchanan, Chester Arthur, Woodrow Wilson and Herbert Hoover.
Mary Anne MacLeod Trump, mother to Donald, was born on the Isle of Lewis in Scotland in 1912, emigrated to the US in 1930, married an American in 1936, naturalized 1942.