The new annual registration fee was first mooted by Glasgow Taxis Ltd (GTL) in September and came into effect this week.
The 700-strong society, which is run by its members, said it needed the cash to help with running costs.
But some drivers, members of the Unite Scotland union, say it is a step too far. More than 500 have signed a petition against the fee.
The union members have slammed GTL for "ignoring" the petition.
Unite representative for the taxi trade, Drew Connelly, said: "They've ignored the level of anger among drivers.
"Taxi drivers are being squeezed beneath the low pay threshold and it's now become standard to work the maximum hours.
"Quite simply, work isn't paying."
"The reality facing many drivers is that jobs will be lost if they cannot pay this imposed £51 fee and they'll be thrown on the unemployment scrapheap all in the name of greed."
However, GTL says that most of the 500 drivers who have signed the petition are not GTL members.
Glasgow has 2000 registered drivers of black Hackneys, 713 are GTL members.
GTL acting secretary, Michael Traynor, said: "The vast majority of our members have paid the £51 fee.
"While we respect the right of Unite's members to protest and to sign a petition, we don't see that they have any right to tell us how to run a business.
"And for Unite to say taxi drivers will be left on the 'unemployment scrapheap' because of this £51 per year, or 98p per week, charge is simply not true."