The Well goalkeeper has been accused of kicking Paterson in the head during the 0-0 draw between the two sides at Fir Park on Saturday.
After viewing the incident SFA Compliance Officer Vincent Lunny charged Randolph with: "violent conduct by kicking an opposing player".
He was offered a fixed two-match suspension, applicable across all competitions, meaning he would miss a Scottish Cup tie with Aberdeen and a league match at home to Ross County.
However, the SPL side have announced their intention to contest the decision, with a SFA judicial panel set to consider the case on Thursday.
A statement on the club's official website read: "Motherwell FC today notified the Scottish FA of the club's intent to contest the fixed two-match suspension offered to Darren Randolph by the Compliance Officer.
"The club lodged the official appeal before 3pm today and the matter will now be referred to the Judicial Panel with a Fast Track Tribunal convened tomorrow (Thursday, 29th November).
"The club will make no further public comment on the matter until that process is complete."