Before you start, I suggest you use the correct format ISO8601, that is 2018-07-11T23:15:15.600Z.
To do the procedure Voce wants Voce will have to implement com.google.gson.TypeAdapter<Timestamp>
Example:
public static class MyDateTypeAdapter extends TypeAdapter< Timestamp > {
    private final SimpleDateFormat dataEhora = new SimpleDateFormat( "yyyy/MM/dd'T'hh:mm:ss.SSS" );
    private final SimpleDateFormat data = new SimpleDateFormat( "yyyy/MM/dd" );
    @Override
    public void write( JsonWriter out, Timestamp value ) throws IOException {
        if ( value == null ) {
            out.nullValue();
        } else {
            if ( value.getNanos() == 0 && value.getSeconds() == 0 && value.getMinutes() == 0 && value.getHours() == 0 ) {
                out.value( this.data.format( value ) );
            } else {
                out.value( this.dataEhora.format( value ) );
            }
        }
    }
    @Override
    public Timestamp read( JsonReader in ) throws IOException {
        if ( in != null ) {
            String dataString = in.nextString();
            final SimpleDateFormat format;
            if ( dataString.length() == 10 ) {
                format = this.data;
            } else {
                format = this.dataEhora;
            }
            Date parsedDate;
            try {
                parsedDate = format.parse( dataString );
                return new Timestamp( parsedDate.getTime() );
            } catch ( ParseException e ) {
                return null;
            }
        } else {
            return null;
        }
    }
}
Now you must create the instance of your Gson setting the created Adapter, see below:
class Exemplo {
    Timestamp dataComHora;
    Timestamp data;
}
class Teste {
    public static void main( String[] args ) {
        Gson gson = new GsonBuilder().registerTypeAdapter( Timestamp.class, new MyDateTypeAdapter() ).create();
        String json = "{\"dataComHora\":\"2018/07/11T11:30:13.795\",\"data\":\"2018/08/11\"}";
        System.out.println( "entrada: " + json );
        Exemplo exemplo = gson.fromJson( json, Exemplo.class );
        System.out.println( "saida: " + gson.toJson( exemplo ) );
    }
}
							
							
						 
It is possible and there are several alternatives ;P As you are doing so far, some specific problem?
– Bruno César
Yes, it is possible, you can register a
type adapterfor the types of time you want to treat, in this post is shown a complete example of how to do it in Gson. http://www.gitshah.com/2011/04/how-to-work-with-json-on-android-part-2.html– Ricardo Rodrigues de Faria