The party raised the issue in the Lok Sabha during the zero hour.
With placards in their hands, TMC Members of Parliament staged a protest in front of a statue of Mahatma Gandhi in the Parliament premises.
TMC leader Derek O'Brien told PTI 34 party MPs took part in the dharna.
West Bengal chief minister and TMC chief Mamata Banerjee had earlier accused the BJP of unleashing an "autocratic rule and destroying the federal structure" of the country and opposed the linking of Aadhaar with mobile phone numbers.
In a TMC Parliamentary party meet, Banerjee had directed party MPs to keep raising the issue to corner the government.