How to work out the seventh day on which it is mustahabb to sacrifice the ‘aqeeqah

It is mustahabb to sacrifice the ‘aqeeqah on behalf of the
new born on the seventh day, because the Prophet (blessings and peace of
Allah be upon him) said: “Every child is in pledge for his ‘aqeeqah, which
should be sacrificed on his behalf on the seventh day, and his head should
be saved and he should be given his name.” Narrated by Abu Dawood, 2455;
classed as saheeh by Shaykh al-Albaani. 

Ibn Qudaamah (may Allah have mercy on him) said: Our
companions said: The Sunnah is to sacrifice it on the seventh day, and we do
not know of any difference of opinion among the scholars who say that it is
prescribed concerning the fact that it is mustahabb to sacrifice it on the
seventh day. The evidence for that is the hadeeth of Samurah, from the
Prophet (blessings and peace of Allah be upon him) according to which he
said: “Every child is in pledge for his ‘aqeeqah, which should be sacrificed
on his behalf on the seventh day…”

End quote from al-Mughni, 9/364 

Secondly: 

Once it is established that it is mustahabb to sacrifice the
‘aqeeqah on behalf of the child on the seventh day, is the day of birth
included in that, according to the majority of scholars? An-Nawawi (may
Allah have mercy on him) said: Is the day of birth counted as one of the
seven? There are two opinions, the more correct of which is that it is
counted, so the sacrifice is done on the sixth day after (the day of
birth). 

The second view is that it is not counted, so the sacrifice
is done on the seventh day after (the day of birth). This is what is stated
in al-Buwayti, but the first view is the apparent meaning of the hadeeths.
If the child is born at night, the day that follows that night is included,
and there is no difference of opinion on this point. 

End quote from al-Majmoo‘, 8/411 

In al-Mawsoo‘ah al-Fiqhiyyah (30/279) it says: The
majority of fuqaha’ are of the view that the day of birth is counted as one
of the seven, but the night is not counted if the infant is born at night;
rather the day that follows that night is counted. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: The
words “is to be sacrificed on the seventh day” mean that it is Sunnah to
sacrifice the ‘aqeeqah on the seventh day. So if the child was born on
Saturday, the sacrifice is to be done on Friday, i.e., one day before the
day on which the child was born. This is the basic guideline. If the child
was born on Thursday, then (the ‘aqeeqah) should be on Wednesday.

End quote from ash-Sharh al-Mumti‘, 7/493 

Thirdly: 

What was said about the day of birth not being counted if the
child is born after midday was stated by a number of scholars (may Allah
have mercy on them). In fact they said that the day of birth should not be
counted at all, whether the child was born before or after midday. This is
the view of the Maalikis. 

It says in Mukhtasar Khaleel: It is recommended to
sacrifice one sheep that meets the requirements of udhiyah on the seventh
day after birth, during the day, and the (previous) day should not be
counted if the birth occurred shortly before Fajr. 

Al-Mawwaaq (may Allah have mercy on him) said, quoting from
Ibn Rushd: The view of Ibn al-Qaasim and his report from Maalik in
al-Mudawwanah and elsewhere is that if the child was born after dawn,
that day is not to be counted, and the seven days should be counted from the
following day. If the child is born before dawn, if that was at night, then
that day is to be counted.

End quote from at-Taaj wa’l-Ikleel, 4/390 

The correct view is that of the majority of scholars (may
Allah have mercy on him), which is that the ‘aqeeqah is to be sacrificed on
the child’s behalf on the seventh day from his birth, because the Prophet
(blessings and peace of Allah be upon him) said: “[it] should be sacrificed
on his behalf on the seventh day…”. 

Shaykh Muhammad ibn Muhammad al-Mukhtaar ash-Shanqeeti (may
Allah preserve him) said: What is meant is that the day of the ‘aqeeqah is
the seventh day after the day of birth. Therefore the day (of the week) on
which he is born is the seventh day.

End quote from Sharh al-Mustaqni‘. 

The matter is mustahabb. If it is possible to sacrifice the
‘aqeeqah on the seventh day after his birth, this is better, but if it is
not possible to do it until after the seventh day, there is nothing wrong
with that and the ‘aqeeqah sacrificed on the child’s behalf will be
acceptable. 

An-Nawawi (may Allah have mercy on him) said: If he
sacrifices it after the seventh day or before it, or after the birth, that
is acceptable, but if he sacrifices it before the birth, that is not
acceptable, and there is no difference of scholarly opinion on this point;
rather it is just meat.

End quote from al-Majmoo‘, 8/411 

And Allah knows best.