In total, 19 men have been arrested and charged over the football-related disorder on April 6 in the Grassmarket area of Edinburgh.
The match between Rangers and Raith Rovers took place at Easter Road stadium. The Fife club won 1-0.
An investigation was launched by Police Scotland after the incident to trace those involved in pre-match disorder.
The men were detained in Glasgow, Renfrew, Edinburgh, Grangemouth, Kirkcaldy and Dumfries on Tuesday and Wednesday.
All have been charged with a breach of the peace and are expected to appear at court at a later date, police said.
Chief inspector Alun Williams said: "The Ramsdens Cup final was a great day out for both sets of fans and the behaviour of the vast majority in attendance was exemplary.
"However, a small minority became involved in disorder within the Grassmarket, causing fear and alarm to other members of the public.
"These actions were totally unacceptable and as a result of joint enforcement activity undertaken by officers from across Police Scotland, several arrests have now been made, with more likely in the coming days.
"We will seek football banning orders in each case and wish to send a clear message that disorder of any form will not be tolerated and anyone found to be responsible for offences of this nature will be robustly dealt with."
Six men have also been banned from football matches for a total of eight and a half years over the incident.
The men were sentenced at Edinburgh Sheriff Court today after they each admitted a breach of the peace charge at an earlier hearing.
Robert Norman Grady, 53, and Craig Lynch, 39, both from Edinburgh, had football banning orders imposed of one year and two years respectively while Gordon McLean, 34, from Glasgow, and Darren Ormiston, 36, from Lasswade, Midlothian, both had one-year banning orders imposed, the Crown Office said.
Two other men aged 38 and 25, who cannot be named for legal reasons, were banned for 18 months and two years respectively.
Speaking after sentencing, Faith Millar, football liaison prosecutor for the East of Scotland, said: "The irresponsibility and selfishness of these men cannot be overstated.
"They engaged in a large-scale fight in the middle of the afternoon in a part of Edinburgh that was busy with shoppers, tourists, and families with young children.
"As prosecutors we will continue to take a robust approach to this sort of behaviour and will continue to work closely with Police Scotland to ensure that the perpetrators are brought to justice."