In this screen capture from video a Turkey Armed Forces convoy is seen at the northern town of Sarmada, in Idlib province, Syria, February 2, 2020. AP
The raids near the Kurdish-held border town of Kobane targeted positions of the Syrian army and the Syrian Democratic Forces, the Syrian Observatory for Human Rights said.
The three casualties were wearing Syrian army uniform, according to the monitor.
Several other fighters were wounded, some in critical condition, according to the Observatory, which relies on a wide network of sources inside Syria.
The strikes were preceded by cross-border shelling from near Kobane against Turkish forces, according to the monitor.
Last month, the Syrian government said it would respond to direct attacks by Turkey against its forces.
The warning came after a Turkish raid on a regime outpost near Kobane killed at least three troops in mid-August, according to the official SANA news agency.
Turkey has launched a series of cross-border offensives targeting Kurdish forces and the Islamic State group since 2016, but such operations have rarely resulted in the killing of Syrian regime fighters.
Ankara has stepped up its attacks in Kurdish-controlled areas of Syria since a July 19 summit with Iran and Russia failed to green-light a fresh offensive against Kurdish fighters viewed by Ankara as terrorists.
Regime forces have deployed in areas controlled by Kurdish fighters near the border with Turkey as part of agreements intended to stem a fresh Turkish operation.
Last week, the UN's Independent Commission of Inquiry on Syria said that "another Turkish ground operation" remains a threat in Syria's north, amid "continued mobilisation and fighting" between Turkish and Turkish-backed forces and Kurdish-led opponents.
"Syria cannot afford a return to larger-scale fighting, but that is where it may be heading," warned Paolo Pinheiro, the head of the commission.