So i had to disconnect and reconnect a few wires to make it easier to install the new brake lines and found this one on the back of the alternator has been burnt and corroded to the point where it snapped off. Any ideas why this would have overheated? any ideas if this is a simple fix of replacing terminal or is it a new alternator?

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2015 Ducati 899 Panigale

Probably a hot joint, caused by a loose connector or frayed wire. Those ones carry a lot of juice. I had to replace one there once.
Or, perhaps the diode bridge rectifier (which those 2 big spades attach) to is buggered. I doubt that though.

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DrMini- 1970 wasaMatic 1360, Mk1S crank, 86.6HP (ATW) =~125 @ crank, 45 Dellorto (38 chokes), RE282 sprint cam, 1.5 rockers, 11.0:1 C/R.

Yes, hot joint.

When joints are dirty or loose, they generate a little heat through resistance (Heat = I^2 x R).
The heat feeds back into the problem and makes it worse by degrading the joint further, so it perpetuates itself.

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SooperDooperMiniCooperExpertEngineering

All garage work involves equal measures of enthusiasm, ingenuity and a fair degree of irresponsibility.