I cant find any solution for this except a dynamic query over the asset table. But this would bypass the search engine from liferay.

I dont know who to ask anymore, is there anyone who can help me with that? 

I just want to serve the liferay default search via REST and JSON.

You can search directly, you can find some sample code in the "Providing a Search Mechanism" part:

https://help.liferay.com/hc/en-us/articles/360018179251-Implementing-Search-and-Indexing

If you want to return any asset type matching your keywords, just build the SearchRequest specifying your keywords. In this example I am reducing the results just to selected documentIds. That documentId is a field of my custom asset type. 

I was trying to build this query using former search API, but I was faced with some class clashes when specifying my terms filter. I rewrote it using new API and those issues have gone. 

So put this dependency to your module:

<dependency>
    <groupId>com.liferay</groupId>
    <artifactId>com.liferay.portal.search.api</artifactId>
    <scope>provided</scope>
</dependency>

And then use something like this
 

@Component(
        property = {
                JaxrsWhiteboardConstants.JAX_RS_APPLICATION_BASE + "=/myapp",
                JaxrsWhiteboardConstants.JAX_RS_NAME + "=MyApp.Rest"
        },
        service = Application.class
)
public class MyRestApplication extends Application {

    @Reference
    protected Queries queries;

    @Reference
    protected Searcher searcher;

    @Reference
    protected SearchRequestBuilderFactory searchRequestBuilderFactory;

    ...
    
    private String getSearchResultsContent(List<Long> selectedDocumentIdList, String keywords, int start, HttpServletRequest request) {

        String content = null;

        try {
            long companyId = PortalUtil.getCompanyId(request);

            SearchRequestBuilder searchRequestBuilder = searchRequestBuilderFactory.builder();
            searchRequestBuilder.withSearchContext(
                    searchContext -> {
                        searchContext.setCompanyId(companyId);
                        searchContext.setKeywords(keywords);
                    });
            searchRequestBuilder.from(start);
            searchRequestBuilder.size(20);
            searchRequestBuilder.highlightEnabled(true);

            TermsQuery termsQuery = queries.terms("documentId");
            for (Long documentId : selectedDocumentIdList) {
                termsQuery.addValue(documentId.toString());
            }

            SearchRequest searchRequest = searchRequestBuilder.query(termsQuery).build();
            SearchResponse searchResponse = searcher.search(searchRequest);

            for (SearchHit hit : searchResponse.getSearchHits().getSearchHits()) {
            }


        } catch (Exception exception) {
            ...
        }

        return content;
    }
};