假設:

DROP TABLE IF EXISTS `table1`;
CREATE TABLE `table1` (
  `id` BIGINT(20) UNSIGNED NOT NULL AUTO_INCREMENT,
  `timemodified` INT(11) NOT NULL,
  PRIMARY KEY (`id`)
) ENGINE=INNODB AUTO_INCREMENT=1 DEFAULT CHARSET=utf8;
INSERT INTO table1 values(NULL,UNIX_TIMESTAMP(NOW()));
INSERT INTO table1 values(NULL,UNIX_TIMESTAMP(NOW())-8640000);
INSERT INTO table1 values(NULL,UNIX_TIMESTAMP(NOW())-1864000);
INSERT INTO table1 values(NULL,UNIX_TIMESTAMP(NOW())-2864000);

全部資料:
select id,timemodified,FROM_UNIXTIME(timemodified) from table1;
結果:

本月: 第一天是前推一個月加一天, 最後一天是本月的最後一天
select id,timemodified,FROM_UNIXTIME(timemodified) from table1 t where FROM_UNIXTIME(t.timemodified) >= DATE_ADD(LAST_DAY(DATE_SUB(NOW(), INTERVAL 1 MONTH)), INTERVAL 1 DAY) and
FROM_UNIXTIME(t.timemodified) <= LAST_DAY(NOW());
結果:

上月: 第一天是前推二個月最後一天加一天, 最後一天是前推一個月的最後一天
select id,timemodified,FROM_UNIXTIME(timemodified) from table1 t
where FROM_UNIXTIME(t.timemodified) >= DATE_ADD(LAST_DAY(DATE_SUB(NOW(), INTERVAL 2 MONTH)), INTERVAL 1 DAY) and
FROM_UNIXTIME(t.timemodified) <= LAST_DAY(DATE_SUB(NOW(), INTERVAL 1 MONTH));
結果:

假設本月份是三月，要查本月份的資料就是日期時間落在 2017-03-01 00:00:00 及 2017-03-31 23:59:59 之間的資料。因此你的 SQL 會是類似
select * from TABLE where timemodified between UNIX_TIMESTAMP('2017-03-01 00:00:00') and UNIX_TIMESTAMP('2017-03-31 23:59:59');