Syria said today it would keep battling Israel's air force for control of the skies over Lebanon despite losing four jet fighters in a dogfight southeast of Beirut yesterday. Israel said it would continue flights over Lebanon and also predicted more aerial encounters.

In the Sinai Peninsula, meanwhile, Israeli forces today turned over to Egypt about 2,500 square miles of territory -- roughly 10 percent of the Sinai -- in the third transfer of occupied land since the Israeli-Egyptian peace treaty was signed in March.

The evacuated area of mountains and deserts, located in the south-central part of the Sinai, borders on the vital Alma oil fields on the Suez Gulf. Those fields are to be handed back to Egypt in two months.

By then, Egypt will have regained half the Sinai. The rest is to be returned in stages by 1982.

The Sinai territory was transferred to the authority of Egyptian Brig. Gen. Safeddin Abu Shnab by Israeli Brig. Gen. Dov Sion in a brief military ceremony at the Abu Durba oasis.

In a commentary on Damascus Radio, Syria said its battle with Israeli planes over Lebanon "will not be the last." The radio said the clash "confirms that Syria is serious in its decision to confront Israel's air force and its dirty mission."

Western military sources in Beirut confirmed that four Soviet-built Syrian Mig 21 fighters were shot down in the dogfight and that no Israeli jets were lost. An Israeli military spokesman said the Israeli planes involved were U.S.- supplied F15s and Israeli-assembled Kfirs.

A section of plane with English writing on it was found late Monday after the dogfight. The Syrians said the fragment was evidence supporting their claim of having shot down two Israeli fighters.

Western military sources said the fragment came from a spare fuel tank that is normally jettisoned when a fighter goes into combat.

A highly placed U.N. source in Lebanon said he did not think the Syrian decision to take on more advanced Israeli planes were merely a flexing of muscles for Arab critics.

He said Syria and Israel both aimed at profiting from the awkward timing of the air battle. In addition to wanting to divert attention from internal unrest which plagues the regime of Syrian President Hafez Assad, Syria is also pushing to assert itself in Middle East politics and the region.

The U.N. source said Syria's action could be seen as a sign it "could draw a red line in the sky," in reference to the imaginary red line along the Litani River, south of which Israel will not permit any Syrian forces.