No one knows where they are.
Professor Aslam Pervez, an historian of Bahadur Shah II's reign and a founding member of the Mughal Trust, told The Daily Telegraph:
"There are so many people who claim to be descended. The Mughals were
scattered, many ran away from Delhi, to Hyderabad, after the mutiny
and no-one knows who went where," he said.
Due to the nature of the deposition of the dynasty, after a violent struggle which saw the massacre of the Royals by the British at the end like the cold-blooded murder by British Commander of the sons of the deposed Emperor:
The princes were mounted on a bullock-cart and driven towards the city
of Delhi. As they approached the city gate, a crowd of people again
started to gather around them, and Hodson ordered the three princes to
get off the cart and to strip off their top garments. He then took a
carbine from one of his troopers and shot them dead before stripping
them of their signet rings, turquoise arm bands and bejewelled swords.
Their bodies were ordered to be displayed in front of a kotwali, or
police station, and left there to be seen by all. The gate near where
they were killed is still called the Khooni Darwaza, or 'Bloody Gate'.
It makes sense that other descendants would have thought it best to flee and spend their days in anonymity for fear of retributions. Pictured below, The Bloody Gate of Old Keep of Imperial City of Delhi, where the corpses of the slain Princes were left to rot, maintained today as a historical artifact.
Same article also reported:
Many are believed to have fled to Calcutta, where 70 descendants have
been traced by the trust, and Aurangabad where a further 200 are
believed to live. Others are believed to be living in Pakistan and
Some of them are living in considerable poverty. One woman, Sultana
Begum, who claims to be the widow of Mirza Mohammed Bedad Baqht,
Zafar's great-grandson, offers a 400 Rupee (£5.40) a month state
pension as evidence.
It appears that Government of India recognizes claim of Sultana Begum as authentic as evident by the payment of token pension to her:
“I get a pension of Rs 400 from the government of India due to the
family lineage,” she said. “I sometimes do odd jobs like wedging
stones in bangles for Rs 20 or 25 a day.” Her husband, Mirza Mohammad
Bedad Baqht used to deal in semi-precious stones.
There are currently efforts underway in India, as stated above, to trace the lost Imperial family by private NGOs. The organizations claim that they have successfully found out 70 lost descandants of Mughals in Calcutta, Bengal state and 200 other descendants in city of Aurangabad alone.
Officially, the Timurid/Khandan-e-Timur/Timuriyan (خاندانء تیموریان) aka Gorkaniyan/Khandan-e-Gorkaniyan (خاندانء گورکانیان) aka Mughal dynasty/Khandan-e-Mughliya (خاندانء مغليہ) ended with the Indian war of independence and the dynasty no longer formally exists and has no head of dynasty unlike many other deposed dynasties which still survive e.g. Osmanlı Hanedanı/خاندان آل عثمان/Ottoman Dynasty.