"Are those Trump's army medals?" another wrote.
Some suggested they might be Trump's bowling and tennis medals, while a few joked that controversial Milwaukee County Sheriff Clarke — who has been accused of wearing "fake pins" on his uniform — lent his collection to the US President.
The coins were actually military challenge coins that would have been given to the President during his time in office.
The coins are produced by the military, law enforcement and fire departments, the Daily Mail reports.
They often feature unique mottos or insignia and are meant to foster unity within the departments or individual units.
The coins would have been given to Trump by different agencies.
During Trump's eight-minute speech, which aired Tuesday night local time, the US President put forward his case for funding a wall along the southern border. He also blamed the partial government shutdown, now in its third week, on Democrats' refusal to fund the gigantic wall.
"The government remains shut down for one reason and one reason only because Democrats will not fund the wall," he told millions of viewers tuning in, pleading with the nation to end what he deemed America's "cycle of suffering".
Democrats have vowed not to appropriate any money for a border wall, which Trump says will cost US$8 billion to build.
"The only solution is for Democrats to pass a spending bill that defends our borders and reopens the government," he said.
