I were unable to find paper with alphabet letters on it to start learning reading/writing in Swiss German. Searched native bookstores and still couldn't find those "1th grade school kids letters typing books". Does anybody know, where could I find such paper, so I could print it and start learning?
After 67 years of teaching a form of cursive ("Schnüerlischrift"), Swiss authorities have recommended substituting it with block letters for all schools in German-speaking Switzerland. As all fonts have slight differences, choosing one common set of letters is important for the benefit of learners. The suggested style is the Luzerner Basisschrift. It's use is recommended, but not mandatory.
The specific charm of the Luzerner Basisschrift is that it comes in varieties, starting as pure block letters, later suggesting "connecting" letters - vaguely resembling cursive - for easier flow and faster writing. The ultimate goal is to develop an individual style of hand that still remains well-legible for others.
You will easily find examples with the help of your favourite search engine or (in German) on the official website of the D-EDK.
Note that other Kantone might demand a different style, you might consider checking with the local authorities to be really sure, especially as the current recommendation is only a few months old.
Different from for example Germany and the US (and many other countries) Swiss primary schoolers start(ed) writing with cursive, namely the "Schweizer Schulschrift" or "Schnüerlischrift" which Carsten S linked to in his comment.