Some times motherboards get it wrong. They are not very accurate.

I experience the same.
One of my motherboards keeps crying about the 12v rail putting out over 16v. When I hook up my multimeter I tried to measure all kind of places on the motherboard, at molex and the 20p connector and P4 connector: the Delta PSU just does its job well.
Hooking up another motherboard to the PSU makes all problems go away: it reports all in spec.
Hooking the "malfunctioning" motherboard to a Sharkoon PSU: again the 16v message in BIOS and multimeter verifies all voltages are in spec.

I used a modern 24Pin power supply.

I found it hard to believe that such PSU has -5v support. Or it's not modern PSU, i.e. not ATX 2.0.

it was the -5v voltage, only having -6.14V.

That usually means that nothing goes to that rail.

Is it causing you any problems?

I bought a P3B-F last year, paired it with a 1GHZ Pentium 3, and ran into some unexpected issues. Every time I tried to use a CD drive the system crashed! There were other symptoms but this was the most obvious. Turned out my 700W relatively modern 80+ gold PSU had some power saving features that meant it didn't supply much 5V power unless there was a significant load on the 12V line. I replaced that with a lower end 80+ 400W PSU and haven't had any power issues since.

SpiceOrange wrote on 2021-03-17, 14:53:

Is it causing you any problems?

I bought a P3B-F last year, paired it with a 1GHZ Pentium 3, and ran into some unexpected issues. Every time I tried to use a CD drive the system crashed! There were other symptoms but this was the most obvious. Turned out my 700W relatively modern 80+ gold PSU had some power saving features that meant it didn't supply much 5V power unless there was a significant load on the 12V line. I replaced that with a lower end 80+ 400W PSU and haven't had any power issues since.

Please share what PSU that was so we can avoid it . From what little I know on the subject, that sounds like a cross load issue .

The Serpent Rider wrote on 2021-03-17, 10:15:

I found it hard to believe that such PSU has -5v support. Or it's not modern PSU, i.e. not ATX 2.0. […]
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I used a modern 24Pin power supply.

I found it hard to believe that such PSU has -5v support. Or it's not modern PSU, i.e. not ATX 2.0.

it was the -5v voltage, only having -6.14V.

That usually means that nothing goes to that rail.

Thanks for this info, I looked online and indeed from the pinout ATX 2.0 does not have -5V.
But in my case, I tested with a PSU I got from a Pentium4 machine as well, and this one does have a -5V, confirmed by the multimeter.
Maybe there is a broken wire from the PSU connector to the monitoring chip. I hope I can get a circuit schematic, so I can test the reading before it goes into that chip(some AD chip I guess).

I have tested with running at 100MHZ, same issue.
I'm waiting for PATA to SATA converter to arrive, before that I can't tell if this is going to cause real issue.

So, to report back, it's actually my mistake, having tested wrong pin.
I took a closer look at the MB power connector, and found out the -5v pin does not have a wire, so it confirms the PSU is an ATX 2.0 PSU.
The reason I got 5v reading on my multimeter was because I tested the wrong side of the two columns, the opposite side of the connector happens to be a Ground and PWR_OK(which is +5v from PSU to indicate PSU is OK).

I tested other things as well, looks to me the board is all good...

Thanks for everyone. And possibly a learning from my mistake..