The LM324/358 you buy from reputable distributors are what you need to work with.

If you can't get them to work properly then you either need to look for a different op amp, or modify the circuit.

 

I have a circuit that works correctly with either an LM358 or a TL072 of which I am sure neither is original. Although on both the pin assignments are the same as the original LM358 and TL072, electrically they exhibit the same behavior as an LM324.

had same problem here,probably with a very similar device.solved it using a Texas Instruments TLC25M2ACP without any other modifications.
it's a bit expensive but if you can afford it, I'm sure it will do the trick.

 

it's been a while since i used through hole IC but the pinout is standard so there are plenty of alternatives, many of them may work without any further change. personally i would look for part that has inputs/outputs that can go rail to rail. or just put IC socket on your board and try couple of products and and see if any of them perform as expected ( MCP6002 , TLV2252IP , NJM2732D ...)

also don't share images through external sites, all of the attachments are already gone.

 

Directly you can rule out AD827, LF353, LM258, LM2904, LM358, LM393, LM741, LT1013, MCP6002, MCP6232, MCP6242, RC4558, TL06*, TL07*, TL08*, TLV2* and such.

NMJ2115, NJM2732, MCP602 may work but with they need extra modifications like, eg, if output has a 100R resistor, replace it with a 330R resistor.

 

No idea. I don't buy dodgy components. I just use proper distributors.

Amen, brother Ian.
My time is more valuable than the (perhaps) extra dollar that a legitimate device costs.

 

Unfortunately there is only one manufacturer and seller of the device and I guess they use the components that work best for them. I don't think they read this site but I don't feel that if they did they would change anything.

probably with a very similar device.solved it using a Texas Instruments TLC25M2ACP without any other modifications.

TLC25M2ACP works like a charm and I have also been able to get it working with MCP602 by adding a resistor.

Thank you very, very much and excuse me if I did not explain myself correctly, I am using a translation service.