When in the arena there are more then 1 player, "score" statistic will auto replacing to "score" statistic another person"

I've just tried and the game is working fine with 1 or more players. What is your server version?

1.20.1

Is there any possibility that you have created 2 instance of the game at the same locations?

I've checked in 1.20.1 and still no problem.

This server is running Paper version git-Paper-196 (MC: 1.20.1) (Implementing API version 1.20.1-R0.1-SNAPSHOT) (Git: 773dd72)
You are running the latest version
Previous version: git-Purpur-1996 (MC: 1.20.1)

What is your server software and try to delete plugin folder and reload the server then recreate an arena.

what you mean about software,i don't understand,is it core?
like spigot?

Yes, can you send the output of /version command.

[14:19:51]
[Server thread/INFO
] [/]:
[14:19:51] [Server thread/INFO]
[/]: Версия плагина СМІ: 9.6.1
0.6 SqLite→> 9.7.0.2
[14:19:51] [Server thread/INFO]
[/]: CMILib: 1.4.5.2 →> 1.4.6.
1
[14:19:51] [Server thread/INFO]
[/]: Версия сервера: Spigot 1.
20.1-R0. 1-SNAPSHOT-
[14:19:511 [Server thread/INF01
[/]: СМІ Экономика: Включено В ерсия Vault: 1.7.3-СМІСМІ Чат:
Выключено
[14:19:51] [Server thread/INFO]
[/]: Модули -> 52 включено 7 о
тключено: flightCharge, chatBub
ble, tablist, votifier, portals , headDrop, playerChatTag

I still couldn't managed to reproduce the issue. Here is the video that I've just recorded.

Try to use a newer fork suh as Paper or Purpur.

no ,score is autoreplacing

@capubara Any updates?

of core?

Did you try with Paper or a newer fork?

No,and i will no do it due to the fact i have mods and i need hybrid core, these guys (Ketting)
are as native for me

Okay then, you can disable scoreboard and use your own scoreboard plugin if you have. You can also use scoreboard placeholders, here is the list of placeholders and scoreboard placeholders.