Farhin,

To ignore base class properties you can ContentApiModelFilter<ContentApiModel> and set the values to null. For this to work you need to set the following property (.SetIncludeNullValues(false)) wherever you are configuring the Content API settings

Below is the example 

    [ServiceConfiguration(typeof(IContentApiModelFilter), Lifecycle = ServiceInstanceScope.Singleton)]
    public class CustomContentApiModelFilter : ContentApiModelFilter<ContentApiModel>
    {
        public override void Filter(ContentApiModel contentApiModel, ConverterContext converterContext)
        {
            contentApiModel.ExistingLanguages = null;
            contentApiModel.Created = null;
            contentApiModel.StartPublish = null;

        }

     }

2. To modify or transform the data being sent back to the client you need to implement DefaultContentConverter and register the custom implementation.

Register the custom implementation in your dependency

.AddSingleton<IContentModelMapper, CustomContentModelMapper>()

Below is an example to make URL's absolute.

    [ServiceConfiguration(typeof(IContentModelMapper), Lifecycle = ServiceInstanceScope.Singleton)]
    public class CustomContentModelMapper : DefaultContentConverter
    {

        public CustomContentModelMapper(IContentTypeRepository contentTypeRepository,
                                ReflectionService reflectionService,
                                IContentModelReferenceConverter contentModelService,
                                IContentVersionRepository contentVersionRepository,
                                ContentLoaderService contentLoaderService,
                                UrlResolverService urlResolverService,
                                ContentApiConfiguration apiConfig,
                                IPropertyConverterResolver propertyConverterResolver)
                            : base(contentTypeRepository,
                                  reflectionService,
                                  contentModelService,
                                  contentVersionRepository,
                                  contentLoaderService,
                                  urlResolverService,
                                  apiConfig,
                                  propertyConverterResolver)
        {
        }

        public override int Order => 200; 
        protected override string ResolveUrl(ContentReference contentLink, string language)
        {
            string resolvedUrl;
            if (_urlResolver == null)
            {
                resolvedUrl = _urlResolverService.ResolveUrl(contentLink, language);
            }
            else
            {
                resolvedUrl = _urlResolver.GetUrl(contentLink, language, new UrlResolverArguments()
                {
                    ContextMode = ContextMode.Default,
                    ForceCanonical = true
                });
            }

            if (string.IsNullOrEmpty(resolvedUrl))
            {
                return null;
            }

            if (!IsAbsoluteUrl(resolvedUrl))
            {
                resolvedUrl = UriSupport.AbsoluteUrlBySettings(resolvedUrl);
            }

            return resolvedUrl;
        }

    }