Yes it is possible to take half day paid leave; there is no arrangement in laws and regulations against it.
According to latest amendment the leave periods may be divided by mutual consent, provided that one of the parts shall not be less than ten days. That means there will be no limitation as to the number of segments by which the leave can be used; employees will be allowed for more flexible use of their annual leave i.e. 10+1+2+1+1. That’s very handy to fill in the gaps between weekends and national holidays as seen in the above example.
Half day paid leave is usually needed before some general holidays.
Turkey has two long national/religious holidays, Ramadan Feast (3 and a half days) and Sacrifice Feast (4 and a half days). In most cases public sector employees are given administrative leaves in the half days between the weekends and mentioned Feasts and extend their off days. However, private sector employees haven't got this chance; and only way to combine the weekends and national holidays is to take their half annual leave in the days between the weekends and mentioned Feasts. It is also valid for 29 October Republic Day, which is 1 and a half day.
It should not be forgotten that employer’s consent is necessary for taking half day paid leave