how to show child documents order by date(a custum field in child page type) in cms?

If you're using DocumentQuery to get child pages, e.g.

var pages = DocumentHelper.GetDocuments()
    .Types("DancingGoat.Article")
    .Path("/Articles/", PathTypeEnum.Children)
    .WhereStartsWith("DocumentName", "Coffee")
    .OnSite("DancingGoat")
    .Culture("en-us")
    .WithCoupledColumns();

DocumentQuery has OrderBy method which allows you to specify a column to sort by.

Also Kentico generates Info and Provider classes for the page types you create, so you could easily get content with Provider class, e.g.

Home homeNode = HomeProvider.GetHome("/Home", "en-us", SiteContext.CurrentSiteName)
                                        .Columns("DocumentName", "DocumentID", "HomeHeader", "HomeTextHeading", "HomeText");

Provider class should also provide you with a method to order the result. See more details here.

thanks Roman Hutnyk, i have asked this for cms documents, in a way that all child documents under a tree node should be ordered according to date provided in custom field...

If you're talking about cms tree (admin section) - they can be ordered only manually.

You could hook into document events and implement some code to order documents the way you need, but I'm not sure it is worth of an efforts.

thanks, Roman Hutnyk