Can I apply for a Dependent Visa as a separated foreign parent of a Thai child with financial constraints?

Chiang Mai has their own requirements list, but here is the general version. You may be able to get a rough idea of what you will need

/7.CHILDREN-OF-THAI-NATIONALITY-NON-O.pdf

okay, first lets get the financial requirements sorted out,

IF you have a half thai child the amount is 400K baht NOT 500K

SO what you're wanting to do is apply first for the Non-O visa based on being the father of a half thai child, and then after that get the year extension for the same reason.

I think your wife will have to go with you for sure, OR you're gonna need a pile of documentation from the hospital why she can't (like that she has stage 4 cancer, etc).

Once in a while they let people who don't have the funds seasoned the 2 months for a yearly marriage extension to get the extension based on raising half thai children, (as there is no seasoning of the funds)

BUT

I can't recall anyone getting the initial 90 day Non-O visa based on being the father of a half thai while still married to the thai mother. <- which doesn't mean it can't be done, just that I can't remember it ever happening 😕

If your office won't do it, you might have to go to a thai consulate (say Savannakhet Lao) and get a 90 day single entry Non-O visa based on being the father of a half thai child, come in get the 90 day stamp,

Then when it runs down apply for the year extension at the immigration office.

What office are you using. Just because someone MIGHT have gotten the Non-O under the conditions you outline IF it wasn't at the immigration office you go to the advice is meaningless, because there are OVER 70 immigration offices in the country