Where can I search for some authors of publications or researchers in a specific filed (e.g. Computer science) and in a specific country (USA, China, ...)
For example I would like to find all people who work on Data Mining located in Iran
I suggest that you use a variant of snowball sampling. Start with the largest, most visible research university in that country (e.g. Iran). Do a web search for the departments most likely associated with the topic (e.g. data mining). Look at the web pages associated with the most prominent researchers. You will find listings of their published papers. In those published papers, you will see co-authors, many from the same university and (importantly) from the same country. Follow the trail of co-authors and repeat these procedures with their web pages.
In a similar fashion, find conference held in this geography. It is likely that there will be a high concentration of local participants and conference committee members. They may or may not be important in the grand scheme, but you will find them.
Using this procedure, you should be able to enumerate 90%+ of the people involved in any one specialty in any one (small) geographic region.
Another approach to get a first set of names is to use one of the large bibliographic databases - Scopus or Web of Science will let you search by affiliation/address. Once you have identified a suitable group of papers (eg by keyword/topic searching) you can filter it to only show papers where at least one author had an Iranian affiliation. You'll then be able to work through these pulling out the relevant authors.
Unfortunately, Google Scholar does not let you search by affiliation and so isn't much use here.
(Scopus, for example, has 9500 papers published since 2014 which match a title/keyword/abstract search for 'data mining', but only 146 of these have an Iranian author)