Check Find Documentation:

https://world.episerver.com/documentation/developer-guides/find/NET-Client-API/searching/Filtering/Custom-filtering-methods/

Filtering by Category:

int categoryId = 3; //Category to match

var pages = SearchClient.Instance.Search<PageData>()
  .Filter(x => x.Category.Match(categoryId))
  .GetContentResult();

Filter by Content Type:

int contentTypeId = 42;

var pages = SearchClient.Instance.Search<IContent>()
  .Filter(x => x.ContentTypeID.Match(contentTypeId))
  .GetContentResult();

We have a similar requirement. Filtering documents using categories..
var pages =  SearchClient.Instance.Search<DocumentFile>()
               .Filter(x => ((IContent)x).Ancestors().Match(pgdata.PageRoot.ID.ToString()))
                .Filter(x =>
                    x.MatchType(typeof(DocumentFile))
                    ).MatchCategories(Catlist)

MatchCategories is a custom filter-  your own filter

Thanks Ram Kumar for your response. 

I've made changes as follows and items in search result is always 0 for some reason. Please let me know if anything wrong in this code. 

public static IContentResult<PageData> MatchCategories(this ITypeSearch<PageData> search, CategoryList cats, string Id)
{
 search = search.Filter(x => ((IContent)x).Ancestors().Match(Id)) 
.Filter<PageData>(x => x.MatchType(typeof(PageType1)) | x.MatchType(typeof(PageType2)) | x.MatchType(typeof(PageType3))));
var catalogBuilder = search.Client.BuildFilter<PageData>();
foreach (var cat in cats)
{
catalogBuilder =
catalogBuilder.Or(x => x.Category.Match(cat));
}
return search.Filter(catalogBuilder).GetContentResult();
}

var result = Helper.MatchCategories(search, currentBlock.FilterCategories, currentBlock.SelectedPageRoot.ID.ToString());

//result.Items returns 0 always

Thanks,

Suresh