Kyle Checkley was in a group of people who ran away when approached by officers working on a drugs operation in the Burngreave area of the city at around 9.20am on July 20 last year.
During Tuesday's sentencing hearing, Sheffield Crown Court was told how the force believed that other members of the group may have been involved in the drugs trade; but Checkley was the only one they were able to trace due to the package of drugs he had left behind.
"What was recovered from the bag, which the defendant had thrown to the floor, was a large number of Class A drugs," said Jane Beckett, prosecuting.
She added: "There were 76 wraps of crack cocaine, and 39 wraps of heroin, which were valued at £1,150 in total."
Checkley, aged 22, was also found to be in possession of £166 in cash and a mobile phone, both of which were seized by police, the court heard.
When interviewed by police, Checkley claimed he had not touched the drugs, which he said belonged to his brother, and that he had won the cash in his possession through gambling.
Ms Beckett said Checkley later admitted he had been street dealing when interviewed by the probation service, but maintained he had a lesser role.
Checkley, of Firshill Walk, Firshill was remanded into custody and committed a further offence in prison, when he was found to be in possession of a mobile phone on August 30 last year.
He pleaded guilty to two counts of possession with intent to supply Class A drugs, and to one count of possessing a mobile phone in prison at an earlier hearing.
Defending, James Gould said: "He is the one who has been arrested, but there are others behind him who are more significant and more involved than he is."
He added: "Since all of this happened he has become a father, and it has changed his outlook."
Recorder Felicity Davies sentenced Checkley to 27-months in prison.
She told him: "It seems that because you were seen to throw something away, you were the one the police honed in on and caught. The others were not caught, and it may be that the ones the police were targeting were not you."
Recorder Davies ordered for the drugs found in Checkley's possession to be destroyed, and for forfeiture of the cash he was found with.