The repeated and diverse efforts by Senator Skelos, a Long Island Republican, to use what prosecutors said was his political influence to find work, or at least income, for his son could send both men to federal prison. If they are convicted of all six charges against them, they face up to 20 years in prison for each of four of the six counts and up to 10 years for the remaining two.

The case against Mr. Skelos and his son grew out of a broader inquiry into political corruption by the United States attorney for the Southern District of New York, Preet Bharara, that has already changed the face of the state capital. It is based in part, according to the six-count complaint, on conversations secretly recorded by one of two cooperating witnesses, and wiretaps on the cellphones of the senator and his son. Those recordings revealed that both men were concerned about electronic surveillance, and illustrated the son’s unsuccessful efforts to thwart it.

Adam Skelos took to using a “burner” phone, the complaint says, and told his father he wanted them to speak through a FaceTime video call in an apparent effort to avoid detection. They also used coded language at times.

At one point, Adam Skelos was recorded telling a Senate staff member of his frustration in not being able to speak openly to his father on the phone, noting that he could not “just send smoke signals or a little pigeon” carrying a message.

The 43-page complaint, sworn out by Paul M. Takla, a special agent for the Federal Bureau of Investigation, outlines a five-year scheme to “monetize” the senator’s official position; it also lays bare the extent to which a father sought to use his position to help his son.