Hayes, who recently joined from first division Norwich City, has signed a two year deal while Parton and Butler have been handed one-year deals.
It is the first professional contract for all three, and shows the clubs continued commitment to youth.
Iron manager Brian Laws said: "We feel that Paul deserved a contract. He has been in the team, scored goals and is a young player who is very confident.
"Hopefully now he has the deal he will score even more goals and become a prolific goal scorer for us.
"At this moment in time he is hot and can certainly go on and have a good career in football."
Neil Collins, Sean Singh and Stuart Preston however have been told that they have not been offered deals to stay with the club.
Laws said: "We have let them know early so they can get some trial games arranged before the end of the season.
"It is a hard decision but I wish them well for the future."