The judge gave the fan, who was identified only as Wesley van der W., an additional two months' suspended imprisonment.
He was also ordered to report to a police station during matches involving Ajax, Alkmaar and the Dutch national team for two years.
The fan attacked Costa Rican Esteban on December 21 during the last 16 Dutch Cup tie between Ajax and Alkmaar, which was abandoned after Esteban was shown a red card for kicking his attacker.
The Dutch football association rescinded the red card a day later and decided this week the match would be replayed on January 19 behind closed doors.
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