WASHINGTON — In the summer of 2015, armed American drones over eastern Syria stalked Junaid Hussain, an influential hacker and recruiter for the Islamic State.

For weeks, Mr. Hussain was careful to keep his young stepson by his side, and the drones held their fire. But late one night, Mr. Hussain left an internet cafe alone, and minutes later a Hellfire missile killed him as he walked between two buildings in Raqqa, Syria, the Islamic State’s de facto capital.

Mr. Hussain, a 21-year-old from Birmingham, England, was a leader of a band of English-speaking computer specialists who had given a far-reaching megaphone to Islamic State propaganda and exhorted online followers to carry out attacks in the West. One by one, American and allied forces have killed the most important of roughly a dozen members of the cell, which the F.B.I. calls “the Legion,” as part of a secretive campaign that has largely silenced a powerful voice that led to a surge of counterterrorism activity across the United States in 2015 as young men and women came under the influence of its propaganda.