The Supreme Court, presided by Nigerian-born Chief Justice Emmanuel Fagbenle, ordered the adjournment because the chief defendant -- the country's Independent Electoral Commission (IEC) -- had not been summonsed to attend.
Jammeh, in power for 22 years, was defeated by opposition candidate Adama Barrow in the December 1 poll.
Barrow's inauguration is due to take place on January 19.
Jammeh initially accepted the result but then reversed position a week later, stoking international concerns about the future of the tiny west African country.
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Jammeh's lawyer, Edward Gomez, informed the court that the IEC had not been served with a summons by Jammeh, the plaintiff.
As a result, Gomez argued, it was in the interest of justice to give time for the IEC to receive the papers requiring it to attend.
"In view of the case that the Independent Electoral Commission is not served, I hereby order that the case is adjourned till 10 January," Judge Fagbenle announced.
"That is all we are saying and at the end of the day it is the ruling of the court that matters. And I believe we will all abide by it and respect it."
Experts say Jammeh has bought time for his bid to stay in office by taking his appeal to a court that has lain dormant since May 2015 and whose judges had been fired under Jammeh's orders save Fagbenle.
Court sources said six foreign judges, excluding Fagbenle, have now been appointed by Jammeh to serve on the Supreme Court.
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