Below are all the steps you have to do.

1)

EXEC sp_changepublication

@publication = 'PublicationName',

@property = N'allow_anonymous',

@value = 'false'

GO

EXEC sp_changepublication

@publication = 'PublicationName',

@property = N'immediate_sync',

@value = 'false'

GO

2) Add table to publication :-

exec dbo.sp_addarticle 'PublicationName' ,@article='TableNeedsToBeAdded',@source_table=' TableNeedsToBeAdded',@destination_table='TableNeedsToBeAdded',

@force_invalidate_snapshot=1

Go

3) Refresh the subscription : -

exec dbo.sp_refreshsubscriptions 'PublicationName'

go

4) Now run the snapshot agent which will only update the object changed/ added new object

exec msdb.dbo.sp_start_job @job_name='JobName'

go