Apart from saying you have an AT3035, you post is a bit short of detail. What is your budget? What make and model is your computer? You mention "recording", so does that mean you pre-record your podcasts and then put them up on the web for download? Do you need your podcast to have any audio in it apart from your voice? You talk about a mixer, but perhaps your idea of using that is to allow you to mix replayed audio in with your microphone channel?

I would leave your mixer out of the loop and look at getting a low-cost but reasonable quality audio interface. A lot of the more modern ones are aimed at podcasters, and have things like talkback loops for live podcasting work. There are literally hundreds of cheap audio interfaces on Ebay, put on there by owners who have upgraded, having painfully realised that you can't get quality on the cheap.

Whoever told you that you can do it cheaper and dont need an interface is, well, not somebody to take advice from! Seriously, you have decided that the Blue Yeti is not for you and you want something that sounds better, so you need an interface. Never a waste, because when you get tired of the AT, you will still need an interface for your next mic, and of course one day you may need two mics, so a basic interface with two channels that also gives you headphone capability is a really good investment. Ask yourself why you dont want to do what 99% of recording folk do every day, take control of your sound. USB mics are great for just one thing, recording one mic. Everything else is your computer. Actually, you do have a sound card, but its a few components on the motherboard costing pennies, and usually very poor quality. Not all, but most. 

Anyway, if your computer doesn't have a sound card, you can use an external sound card, big or small. I'm not sure about your microphone model, but I think your idea is feasible.

Thank you everybody for your ideas and suggestions. First let me answer Boswell's questions: I am working on a YouTube educational video course. I treat it as a hobby and since I have a special skill to make math easy to learn I would like to share it with others. This is not a commercial project and since I live on a medical disability check I don't have any budget for equipment upgrade. The sound of Blue Yeti is not terrible but not the best. All what I need to record is my voice as a narrator. A small issue is that I don't have a tripod which can hold Blue Yeti and it is a bit awkward to use it while delivering a lesson. Ones upon a time I bought AT3035 with a mixer to record a grand piano and reading reviews I got an idea that AT3035 should sound better than the Yeti plus I have a tripod for it. 

For the last month I was preoccupied by making animations with PowerPoint for formulas illustrations and now I am back to video recording. In the mean time I got some development: first I connected my previous computer which has a line in jack as well as very old Windows 7 system which at that time had a 7.1 channel sound card which suppose to be good. At the same time I bought based on ChatGPT advice U-Control UCA222 to connect between computer and Behringer mixer because it was very cheap on Amazon. Now I am going to play with all of those combinations to see if I can get better sound then from the Yeti. On the other hand I figure out that Yeti can be directly connected to my Galaxy S24 Ultra which I use as a camera which is way more convenient than trying to record in Audacity and then trying to sinch everything in a video editor.

Any additional advice will be greatly appreciated.

The Samsung S24 Ultra has a wonderful set of cameras, and it also has the capability of using an external microphone, including certain types of USB microphone. One has to assume that the external microphone will work with the video app, since this does not appear to be stated anywhere.

The S24 Ultra is not a cheap item, and doesn't easily fit with your story about not having any budget that could be used for better quality audio gear. However, if you can get your Blue Yeti to work with it (USB A to C adapter cable needed), you may be able to by-pass the need for a mixer and the UCA222, which would be a bonus.

Boswell,

You said: "The S24 Ultra is not a cheap item, and doesn't easily fit with your story about not having any budget that could be used for better quality audio gear." It sounds that is it not but a couple of month ago Costco had a promotion that Galaxy S24+ was free if you trade in any galaxy any year any condition which I did. In addition at gave me $100 cash rebate to cover $70 sales tax which I had to pay, so new was about $30 gain. However, since I choose Ultra I am paying $8 per month for 36 months which I decided worth it considering quality of the cameras on it.

"However, if you can get your Blue Yeti to work with it (USB A to C adapter cable needed), you may be able to by-pass the need for a mixer and the UCA222, which would be a bonus.". Since I already have UCA222 - do you think I can connect AT3035 via mixer via UCA333 to the S24? Last thigh which I want to do is to ruin my Galaxy.

I don't know what a UCA333 is, but I doubt whether the S24 Ultra would be able to recognise either that unit or the UCA222 that you say you have,

I would have thought that your best bet is to try using the Blue Yeti via a USB A-C cable. If that works, look around in second-hand stores and auction sites for a mic stand that would hold the Yeti at a usable height. What may happen is that you get the left channel working but no sound in the right channel, even with the polar switch on the Yeti set to the stereo pattern.