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16 Psyche is theorized to be the remnant iron core of an early small protoplanet that might have had it's surface and mantle stripped away through violent asteroid impacts.

Some modeling of possible magnetic fields and solar wind disruptions from 16 Psyche have already been performed in this paper. Here is one of their figures:

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This question is a follow on to this idea: Place a satellite at Sun-Mars L1 to shield Mars from Sun radiation . If we could put the enormous iron asteroid 16 Psyche at Mars L1 and spin it up, could we shield Mars from solar winds?

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No. Spinning an asteroid won't generate a magnetic field.

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    $\begingroup$ What if it's magnetized? $\endgroup$ Dec 3, 2020 at 17:20
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    $\begingroup$ The composition is far from ideal as a permanent magnet. I would be surprised if you couldn't get better results with a much smaller (and vastly lighter) superconducting loop. $\endgroup$ Dec 3, 2020 at 17:37
  • $\begingroup$ So, the above linked paper: "Solar Wind Plasma Interaction with Asteroid 16 Psyche: Implication for Formation Theories" is incorrect? $\endgroup$ Dec 3, 2020 at 17:43
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    $\begingroup$ @ConnorGarcia I don't see anything in that paper that compares it to possible artificially produced magnetospheres or claims it would be suitable for shielding Mars. In fact, the simulated magnetosphere looks like it's a fraction of the diameter of Mars. $\endgroup$ Dec 3, 2020 at 18:49
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    $\begingroup$ @uhoh the quadrupole or just an overall charge would technically produce a magnetic dipole, but I think the charge would have a bigger effect on the solar wind than the magnetic field at any plausible rotation rate. A thundercloud on Earth can have a net charge of 350 C, that charge traveling in a loop at the rotation rate of Psyche would constitute a current of 23 milliamps. $\endgroup$ Dec 4, 2020 at 0:39
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I believe what you might be thinking of is called a "dynamo"... and yes, IF we could create a dynamo with an intense enough field and IF we could control the orientation of the dynamo relative to the direction of the solar wind - it would FULLY be possible to create a ((love your word:)) magnetosheath for Mars.

So your answers are: No, not with 16 Psyche, but Yes with something else it would be possible.

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