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If there is not a channel for the clips to attach to then it sounds like you have a self-rimming drop-in sink without clamps.
This type of sink is installed by placing it into the counter top cutout with the rim of the sink resting on the counter top. A bead of caulking is applied around the edge of the entire sink to hold the sink in place and to provide a water tight seal.
Unfortunately, clips are not going to work with the type of sink that you have because there is no place to attach the clips to on the bottom of the stainless steel sink.
Feel free to post any follow-up questions you may have.
You can use an all purpose adhesive caulk to provide the bond and seal needed.
Attached is a link to the product for your review. This typically can be found at any home improvement store.