What happened to some native americans during the jackson presidency?

they were to leave their homeland and move westward.
they allied themselves with slaves to seel equal protection under the law.
they were given large land grants on their native soil.
they filed a large number of lawsuits to protect their rights.

Jackson was president for 8 years, from March 1829 until March 1837. A lot happens in
8 years, so I am overwhelmed by your question, but I mention few things.

The state of SC, hurt by the federal tariff, propounded the doctrine of nullification when
meant that states could, after due action by their government annul federal laws and
not obey them-- and if the government tried to enforce the laws anyway, the states
had the right to leave the federal union. Although Jackson fought to squelch this idea,
it arose again in 1860 when SC actually seceded from the union, provoking the
Civil War.

The second national bank of the US was abolished and the Presidential election
of 1832 became essentially a plebiscite vote on this issue.

The Indian act set processes in motion to move the Indians living in GA and Alabama
westward to AK and OK.

President Jackson used the veto power of the president in a new way, The 6 previous
presidents had only used the veto when they thought a bill was unconstitutional. Jackson
believed that he should veto any bad bill which was against the interests of the people
even if it was constitutional. Consequently , Congress began asking what the president
would like before they proposed or passed laws. Such was the case for previous
presidents. Before Jackson, the presidents let the Congress make the laws without any
interference from the Whitehouse.

Americans living in Mexican controlled Texas, revolted, declared their independence,
were put down by the Mexican dictator, fought back and applied for statehood in the US.
Eventually there were given statehood ,leading to war with Mexico.
Also the Chereokee Indians were forced to move do to the Indian Removal Act mention above but they did no move until 8 years after the act was establish. This walk was called THE TRAIL OF TEARS.

The answer said by blackbullet2000 is right