select records from postgres where timestamp is in certain range

Another option to make PostgreSQL use an index for your original query, is to create an index on the expression you are using:

create index arrival_year on reservations ( extract(year from arrival) );

That will open PostgreSQL with the possibility to use an index for

select * 
FROM reservations 
WHERE extract(year from arrival) = 2012;

Note that the expression in the index must be exactly the same expression as used in the where clause to make this work.

SELECT * 
FROM reservations 
WHERE arrival >= '2012-01-01'
AND arrival < '2013-01-01'
   ;

BTW if the distribution of values indicates that an index scan will not be the worth (for example if all the values are in 2012), the optimiser could still choose a full table scan. YMMV. Explain is your friend.

Search till the seconds for the timestamp column in postgress

select * from "TableName" e
    where timestamp >= '2020-08-08T13:00:00' and timestamp < '2020-08-08T17:00:00';