I tried to google it, but it seemed to be lack of sensible answer. So, I ask you questions:
What is a meaning of suffix "nip" in "Catnip"? and Where is it come from?
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Catnip comes from cat + nip, where nip comes from nepte. Here nepte is the Old English name of catnip or of a family of herbs including catnip, and originally comes from Latin nepeta (with the same meaning).
As @peter-shor's answer says already : nip [...] comes from Latin nepeta [...] family of herbs. Regarding the source of the nepeta genus, quoting Floral Centric [...] by William Darlington in 1826:
Nepeta the Latin name, from Nepi, Italy
"Nip" comes from Germanic words that suggest holding or pinching. The root is Indo-European. It can be seen in OLD Norse and Dutch with almost the same meaning. The word currently being used in Punjabi 'nup' has the same meaning. If a cat is attracted to the smell that comes from catnip, the olfactory sense holds the cat in bondage.