This should help you get started. Please note how I created a table and populated that table with sample data. This is what you need to provide in the future when posting questions like this. I do have to give you credit for also posting the expected results as that is needed as well.

create table #TestTable (

PatientName varchar(132),

ApptNumber int,

ApptDate datetime

);

insert into #TestTable

values

('John Smith',18374832,'2012-01-05 08:15:00'),

('John Smith',19837289,'2012-01-07 14:30:00'),

('John Smith',19982776,'2012-02-15 09:00:00'),

('John Smith',20091092,'2012-02-27 15:45:00'),

('John Smith',20100939,'2012-02-28 07:25:00'),

('John Smith',20110938,'2012-03-05 16:50:00');

with BaseData as (

select

PatientName,

ApptNumber,

ApptDate,

rn = row_number() over (partition by PatientName, dateadd(mm, datediff(mm, 0, ApptDate), 0) order by ApptDate asc)

from

#TestTable

)

select

PatientName,

ApptNumber,

ApptDate

from

BaseData

where

rn = 1;

drop table #TestTable;

/*

Given that data the query will only return:

John Smith 18374832 2012-01-05 08:15:00

John Smith 19982776 2012-02-15 09:00:00

John Smith 20110938 2012-03-05 16:50:00

*/