Could anybody please clear this doubt for me?

"Can anybody tell me what was it that the General felt towards Caspian in that scene when he refuses to kill him?"

I am not sure that he wouldn't have killed Caspian. My guess is that he was just fighting all of the Narnian creatures and animals that suddenly he sees the familiar face of Caspian. Technically, at that time, Caspian was the king as Miraz was dead and Caspian was the next in line to the throne.

I think the General's name was Sopespian. He was one of the two top Generals of Miraz but did not like the ways of Miraz, who killed his way into power, or Glozelle, who likewise would kill to gain power. He was contemplating whether to kill Caspian who had spared Miraz's life.

Bob

General Glozelle. Well, this guy knew the truth about Miraz, having been ordered by him to murder Caspian at the very beginning of the film and to sacrifice his own men at several points in the story later on. He certainly wouldn't mind Miraz being gone. So when he came face to face with Caspian, he probably thought, "Wait - why am I about to kill this kid who's the true king, and I should really be loyal to?". The guy was just a soldier following orders, and with Miraz dead he had no reason to fight on the wrong side anymore.