Hi VR,
Let us say your table has around 10 records with different countries in it. and you apply filter criteria and you can filter like Ind*, etc. .. as you say its working fine
For filter help, refer the link Web Dynpro ABAP - Filtering in Table UI element
Now, coming to search criteria, are you looking for search help for the editor of column "country", then its same as normal field's search help , you can go ahead with OVS, Standard search help for country data element.
Refer the below link:
[Web dynpro] Dictionary search help v/s OVS
Hope this helps you.
Regards,
Rama