"There are three drones which hover above my village 24 hours a day… it's the Americans, I'm sure of it. They've killed Bin Laden and now they're after my son."

Nasser al-Awlaki is a worried man. He fears for the life of his eldest son, Anwar, the US-born civil engineer turned radical Muslim cleric who is now the spiritual guru of al-Qaida's most active franchise, al-Qaida in the Arabian Peninsula. With Bin Laden's death, some officials believe Anwar and the Yemen-based group now represent the gravest threat to the US.

Last spring, Barack Obama authorised the killing of Awlaki, believed to be in hiding with tribal leaders in the rugged southern region of Shabwa, after he was linked to a US army psychiatrist who killed 13 people in Fort Hood, Texas, in November 2009 and then to a Nigerian student accused of trying to blow up a Detroit-bound passenger jet on Christmas Day that year.

On Thursday the US launched a missile strike from a drone on a village close to Nasser Awlaki's hometown in Shabwa, incinerating a car along with two alleged al-Qaida militants. US and Yemeni officials later claimed that Anwar had been the intended target but that he evaded the missile.

The bushy-bearded American-born preacher, though not one of the group's senior leaders, is seen by the west as one of al-Qaida's rising stars; a charismatic, internet-savvy individual with a knack for making firebrand anti-western sermons and using Facebook and YouTube to exhort Muslims around the world to kill Americans.

"They [the western media] have claimed he's going to be the next leader of al-Qaida, but it's nonsense. Anwar is not a leader, he's just a man with strong views and a big mouth," said his father, who has served in Yemen's ruling party as agriculture minister.

Whether he succeeds Bin Laden or not, Awlaki and his YouTube sermons nod to the importance of Yemen's own disparate al-Qaida branch, one which shares Bin Laden's austere and chauvinistic Salafi brand of Islam, but which is nevertheless autonomous and more internationally engaged than the old core of al-Qaida in Pakistan.

Yemen's weak central governance, rugged terrain, and widespread poverty have given militants significant elbow room over the past few months in tracts of the south-east where they have been able to thrive despite a barrage of airstrikes and raids by President Ali Abdullah Saleh's US-trained counter-terrorism forces.

But despite the group's own near daily assaults on Yemeni security forces, local experts insist that al-Qaida here remains a fringe group with 100 to 200 hardcore fighters and a few hundred Yemenis giving them support.

"Al-Qaida represents a very, very small minority in Yemen, but they are self-ruling, committed and incredibly well organised," says Saeed Obeid, a Yemen expert and writer on al-Qaida. "As such the death of Bin Laden has had little or no effect on their current operations."

While the Yemeni government was quick to praise the US raid on Bin Laden, the response on the streets of Sana'a, where protesters have been staging vibrant demonstrations against Saleh for more than three months, has been muted.

"We're not interested in Osama bin Laden," said Ajaa al-Rafhdi, an opposition protester at Sana'a's Change Square. "This is just one man. Our fight is against Ali Abdullah Saleh."

But while the end of the US's 10-year manhunt may not elicit a strong response from the street, some believe it will create a chance for the president to retain the office he has held for 33 years. The US has cultivated Saleh as an ally in its fight against al-Qaida, more than doubling its military aid to $150m last year. The president recently warned the US that his departure would mean gains for the terrorist group.

Demonstrators claim that for years Saleh has allowed al-Qaida affiliates to thrive and launch attacks in order to reap the political and financial benefits. Now, as Saleh appears to have backed out of a second Gulf-sponsored initiative that would see him exchange power for immunity, he may be looking to capitalise on Bin Laden's death.

"Terrorism in Yemen relies on a lack of clarity, and on grievances caused by a corrupt and incompetent regime," said opposition party leader Hasan Zaid. If Saleh's government were replaced, he said, "the dark holes in society in which these groups seek refuge will be lit up, and their resources and appeal would be diminished".