About: “Fixed Amount Tax Reduction Supplementary Benefit (Adjustment Benefit) Deficiency Benefit”

I got some papers from my ward office some time ago, telling that if I'm eligible for this benefit, I should apply. The Japanese title of the online page where I can apply is "定額減税補足給付(調整給付)不足額給付金"

I did some research myself and then asked my employer company's tax accountant, but I couldn't get any clear answer. I was wondering if anyone went through this and has an idea.

I came here and started working at March 2024, due to it being my first year, I didn't pay resident tax. This year, resident tax started getting cut from my salary, which I can see on my payslips.

I've read that in 2024 (2023?) there were some tax cuts, and since low income families pay low tax, they didn't benefit from tax cuts, therefore the ward office directly paid them some amount so everyone benefited from tax cuts. At first I thought since I didn't pay resident tax on my first year, I also didn't benefit from tax cuts so I might be eligible, but then the amounts for that one and the amount for the one I'm asking here seems very different. The online application page says I'll be paid either 0 or 10000 (depending on the value I enter into field "お問い合わせ番号", while the tax cut I mentioned was 30000 per person living in the same household, so I think this is a different matter.

Anybody has an idea? I don't want to get some money that I'm not eligible for and later go through procedures to give it back. As the amount of money is not that large, I'm mostly asking to learn what is going on, before I give up and not get anything.