This is the log I got when trying to launch any game on any Fabric Version that was compatible

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Version does not support log configuration, will assume one plaintext entry per line
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[11:12:25] [INFO] [FabricLoader/GameProvider]: Loading Minecraft 1.20.1 with Fabric Loader 0.16.14
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[11:12:25] [WARN] [FabricLoader/GameRemap]: Incomplete remapped file found! This means that the remapping process failed on the previous launch. If this persists, make sure to let us at Fabric know!
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[11:12:25] [INFO] [FabricLoader/GameRemap]: Fabric is preparing JARs on first launch, this may take a few seconds...
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[11:12:25] [ERROR] [FabricLoader/]: Uncaught exception in thread "main"
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java.lang.RuntimeException: error remapping game jars [F:\Modded MC\curseforge\minecraft\Install\versions\fabric-loader-0.16.14-1.20.1\fabric-loader-0.16.14-1.20.1.jar]
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at net.fabricmc.loader.impl.game.GameProviderHelper.deobfuscate(GameProviderHelper.java:249)
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at net.fabricmc.loader.impl.game.minecraft.MinecraftGameProvider.initialize(MinecraftGameProvider.java:331)
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at net.fabricmc.loader.impl.launch.knot.Knot.init(Knot.java:140)
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at net.fabricmc.loader.impl.launch.knot.Knot.launch(Knot.java:68)
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at net.fabricmc.loader.impl.launch.knot.KnotClient.main(KnotClient.java:23)
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Caused by: java.io.IOException: the jar file F:\Modded MC\curseforge\minecraft\Instances\Prominence II Hasturian Era.fabric\remappedJars\minecraft-1.20.1-0.16.14\client-intermediary.jar.tmp can't be written
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at net.fabricmc.loader.impl.lib.tinyremapper.OutputConsumerPath.(OutputConsumerPath.java:102)
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at net.fabricmc.loader.impl.lib.tinyremapper.OutputConsumerPath.(OutputConsumerPath.java:42)
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at net.fabricmc.loader.impl.lib.tinyremapper.OutputConsumerPath$Builder.build(OutputConsumerPath.java:74)
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at net.fabricmc.loader.impl.game.GameProviderHelper.deobfuscate0(GameProviderHelper.java:305)
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at net.fabricmc.loader.impl.game.GameProviderHelper.deobfuscate(GameProviderHelper.java:247)
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... 4 more
11:18:16.920
Process crashed with exit code 1

Caused by: java.io.IOException: the jar file F:\Modded MC\curseforge\minecraft\Instances\Prominence II Hasturian Era.fabric\remappedJars\minecraft-1.20.1-0.16.14\client-intermediary.jar.tmp can't be written

Fabric does not have the neccessary permissions to write to your F drive. You´d need to fix that permission issue yourself