create table links (
id int primary key auto_increment
);
insert into links values (1);
create table blocks (
id int primary key auto_increment,
link_id int,
t text
);
insert into blocks (link_id, t) values
(1, 'Block1'), (1, 'Block3'), (1, 'Block3');
select *
from blocks
join (
select min(b.id) id
from blocks b
join links l on b.link_id = l.id
where l.id = 1
) fb on fb.id = blocks.id