Some protesters threw fireworks and Molotov cocktails as they engaged in street battles with police, who used water cannon and tear gas, in the Istanbul district of Okmeydani, an AFP photographer reported.
The activists were marking the first anniversary of the death of Berkin Elvan who died on March 11, 2014, after spending 269 days in a coma due to injuries sustained when he was hit by a tear gas canister fired by police in the mass protests of early summer 2013.
"Protests took place in some 20 cities in Turkey, local media reported, while the slogan "Seni Unutmadik Berkin Elvan" (We have not forgotten you, Berkin Elvan) was trending strongly on Twitter."
He was aged 15 at the time of his death, which was followed by mass nationwide protests that were also largely put down by the police.
The worst of Wednesday's unrest came in the district of Okmeydani, the former home of Elvan, where hundreds of supporters attempted to stage a march but were thwarted by police tear gas and water cannon.
Earlier, police had moved in to arrest a handful of protesters in Taksim Square in central Istanbul who joined hands and unfurled a banner reading "Berkin is here".
In the capital Ankara, police also used water cannon to break up a protest, arresting 11 people, local media said.
Meanwhile, vandals attacked a small statue of Elvan that had been unveiled only last week in the Guzelbahce district of the western city of Izmir.
The damage left a crack across the head of the statue, in a possible reference to Elvan's own injury, Turkish media reports said.
Protests took place in some 20 cities in Turkey, local media reported, while the slogan "Seni Unutmadik Berkin Elvan" (We have not forgotten you, Berkin Elvan) was trending strongly on Twitter.
Elvan's death brought to eight, including one policeman, the number of people confirmed to have died during the protests in May-June 2013.
A man points his gun in front of a barricade towards Turkish riot police with a pistol on March 11, 2015 in Istanbul, during clashes following a protest in memory of a teenager killed in 2013 anti-government demonstrations and whose death has become a rallying cause for opponents of President. AFP PHOTO
The demonstrations began as an action against the redevelopment of Gezi Park adjoining Taksim Square in Istanbul but snowballed into a full scale nationwide wave of protest against Erdogan, who was then premier.
Elvan's parents and supporters are furious that no police officer has been brought to trial over his death, accusing the authorities of concealing the name of the perpetrator.
Elvan
They say he was not even actively protesting but was caught in the turmoil in Istanbul after going out to buy bread.
A Turkish police officer went on trial in December 2014 after he went on Facebook to praise the killing of Elvan, saying: "I kiss the hands of the riot policeman who fired on your head".
Erdogan had sparked an outcry after he called Elvan a thug with links to a "terrorist organisation" and encouraged his supporters at a rally to boo Elvan's mother.
The president is accused by opponents of seeking to use his powers to turn Turkey into a police state, in particular through a controversial security bill that is currently the focus of angry debate in parliament.
The bill notably permits police to use firearms to prevent an attack in a public place against people using Molotov cocktails or similar weapons.
Those in possession of such objects at protests would face up to four years in jail. The bill also calls for stricter punishment for offenders wearing masks to conceal their identity.