The All-India States’ Peoples’ Conference (AISPC) was a federation formed in 1927, comprising political movements in princely states of British India. The objective was to bring together the voices of these states and act as a front to demand their political and administrative rights.

Option 1, Jay Prakash Narayan, was a renowned Indian independence activist and political theorist but did not hold the presidency of AISPC in 1939.

Option 2, Jawaharlal Nehru, is the correct answer. In 1939, he was elected the president of the All-India States` Peoples` Conference and played a vital role in voicing the aspirations of the people of the princely states.

Option 3, Sheikh Abdullah, although a prominent politician of Jammu and Kashmir, didn`t hold this position.

Option 4, Sardar Vallabhbhai Patel, one of the leading figures in the Indian National Congress and a key player in the country’s independence struggle, was not the president of AISPC in 1939.

In summary, the president of the All-India States` People`s Conference in 1939 was Jawaharlal Nehru.