I live on the second floor of my house Every time I use my kitchen sink the sink from the first floor apartment directly below me gets stopped up and water starts rising from their sink. Thre is no problem with the toilets or bathroom sinks in the house only the kitchen We tried snaking both sinks and mister plumbing in both sinks. This has been going on for a few days now

Clog somewhere after the first floor apartment. Follow the drain line to a main line cleanout and start there. If the tub is before the sink, it will back up too since it is lower than the sink.

It tells me you share your kitchen drain with bottom apartment. Bottom apartment has blockage in the common portion of the drain. Have it snaked ( cleaned ).

Milo

We tried snaking both sinks

Snake the lower sink again. Some times you can have a soft blockage that closes up as soon as you pull the snake out. If you are using a manual snake try a powered snake.

If you can run a small amount of water in the upper sink and not have it come out the lower sink pipe while you are snaking, that may help to wash away the blockage.

In addition: use proper tip for snaking kitchen sink drain. If you don't, as you pull the cable out, the sludge will enclose the opening as it was before the snake was inserted.

Moreover, the blockage is most-likely further down the drain. 15' cable may not be long enough to reach the blockage. For these situations, we usually use 3/8" x 50' cable and run it ( if possible ) entire length.

Once you remove the snake, run hot water for several minutes in the sink to flush down any loose debris inside the drain

Milo

Was this home originally built with kitchens on both floors? Wondering if it's a remodel and someone used the vent was a wet drain. Advice is all good, clog is further downstream.