Hariam Barzan, 25, and Ayman Barzan, 18, were detained by police on holiday after being quizzed over their alleged support of the Syrian Kurdish People’s Protection Units (YPG) militia.
Photos posted on social media by the brothers several years showed the group’s flags in the background.
The YPG is fighting the Islamic State (ISIS) in Syria but is blacklisted as a terror organisation by Turkey, although not by the rest of Europe and America.
Officials at Dalaman Airport found the photos when the brothers arrived in the country at the start of July.
Although of Iraqi origin, the brothers are British nationals who grew up in the Regents Park area of Wakefield’s Eastmoor estate and attended City High School.
They now live in London and had been visiting Turkey to celebrate Hariam’s 25th birthday and meet up with their sister.
They have not been given a trial date and more than 1,000 people have since signed an online petition on change.org to free them.
A friend of the men, who has known them since they were young, told the Express this week: “They (their family) are worried about their health, with torture and abuse in the prisons as there is a lot of discrimination against Kurds in Turkey.
“They are also worried about their studies as Hariam is in university and Ayman is in college. They have not been charged officially just waiting on court dates.
“Ayman is typical teenager who lives for football and has excelled in his studies, while Hariam is also studying and working.
“He has always kept himself to himself and stayed away from trouble to focus on work.”
The Foreign Office confirmed this week that they are in contact with the Turkish authorities over the brothers’ detention.