Tebyiah said the only way to bring his children to Turkey, which was closed to fleeing Syrians earlier this year, is to pay smugglers US$500 for each child, money he does not have.
"I have to find a solution as soon as possible or I don't want to think what will happen."
Fighting intensified in Syria's second city last week, in violence which has left more than 250 dead and, to many eyes, effectively ended the much-publicised ceasefire which had largely been holding since February.
Now the opposition-controlled eastern side of Aleppo is braced for an all-out offensive by the Syrian Government and its Russian and Iranian allies, that could change the course of the conflict.
As the bombs dropped on the city, residents wondered where their supposed protectors, the Americans, were. Many had been optimistic that the ceasefire, brokered by the United States and Russia, was the ray of hope the city needed after suffering an unparalleled, blistering four-year campaign of violence.
Just a few weeks in, they found the bombs were dropping once more.
Moscow had declared that as the east of Aleppo was under the control of jihadist rebels, such as the al-Qaeda-linked Jabhat al-Nusra, it should not be covered by the truce.
"The fighting there is very alarming," a US State Department spokesman said when asked why the US did not try to get a halt to the growing violence in Aleppo, "but the situation is very complex."
Aleppo was Syria's commercial hub before the war broke out five years ago, home to two million people. Because of its strategic location near the Turkish border, and symbolic significance, it is often said that whoever holds Aleppo wins the war.
Neither side has managed to fully control it since opposition forces took parts of the east in 2012.
President Bashar al-Assad and his troops have for months been working up to what they are calling a "war of all wars" to retake it from the rebels.
John Kerry, US Secretary of State, had said if the ceasefire and peace talks in Geneva collapsed, America would move to "Plan B", which included supplying moderate rebels with weapons, such as shoulder-fired anti-aircraft missiles, to counter Russian warplanes.