14 staffers of Cumhuriyet, some of the few remaining voices critical of the government, were sentenced in April 2018 to jail terms of up to eight years.
They were also sentenced to one month on charges of terrorism and supporting U.S.-based cleric Fethullah Gulen.
They were similarly condemned for organising the 2016 attempted coup.
All the defendants, some of whom had been in prison for the duration of the trial, had been released pending an appeals process.
In February, another court rejected their appeals.
All the accused have denied the charges against them and argued the case is political and aimed at silencing opposition voices.
Gulen denies any involvement in the coup attempt.
Six Cumhuriyet staffers, whose sentences are less than five years, was returned to jail to serve out their terms.
Two others who were also sentenced to less than five years will remain free due to the time they served as the trial continued.
Tora Pekin, a lawyer for the defendants, said during a news conference on Monday that the appeals court had not granted their request for a hearing ahead of deciding whether to uphold the sentences.
Abbas Yalcin, another lawyer, said they had requested the sentences be suspended and were waiting for the request to be evaluated by the court.
Human rights organisations have voiced increasing concern about media freedom in Turkey, accusing Erdogan of using the abortive putsch as a pretext to quash dissent.
Since the failed coup, over 77,000 people have been jailed pending trial, while about 150,000 civil servants and military personnel have been sacked or suspended from their jobs.
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