Here are the steps to add article in publication without setting up whole replication again or running the whole snapshot again.

First Execute these two statements :-

To Get the publication Name:-

exec dbo.sp_helppublication

EXEC sp_changepublication

@publication = 'PublicationName',

@property = N'allow_anonymous',

@value = 'false'

GO

EXEC sp_changepublication

@publication = 'PublicationName',

@property = N'immediate_sync',

@value = 'false'

GO

Add table to publication :

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

@force_invalidate_snapshot=1

Go

Refresh the subscription : -

exec dbo.sp_refreshsubscriptions 'PublicationName'

go

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

How to find out the Snapshot agent job name:-

Select Name From MSDB.dbo.sysjobs