Times one should sleep or take a nap
Allah() says in the Qur'an:
O you who have believed, let those whom your right hands possess and those who have not [yet] reached puberty among you ask permission of you [before entering] at three times: before the dawn prayer and when you put aside your clothing [for rest] at noon and after the night prayer. [These are] three times of privacy for you. There is no blame upon you nor upon them beyond these [periods], for they continually circulate among you - some of you, among others. Thus does Allah make clear to you the verses; and Allah is Knowing and Wise. (24:58)
These tree times are the recommendations for having a rest: before dawn (fajr) prayer, after the dhohr (noon) prayer and after the 'isha' prayer as practiced by the prophet ():
Allah's Messenger (ﷺ) disliked to sleep before the `Isha' prayer and to talk after it. (Sahih al-Bukhari)
In my house he (Prophet (p.b.u.h) ) never passed the last hours of the night but sleeping. (Sahih al-Bukhari)
“Take a siesta for the devils do not take a siesta.” Narrated by Abu Na’eem with a saheeh isnad. Saheeh al-Jami’, 4/147. (Source islamqa #21052)
You should try to take a rest at does times as they are the most recommended times.
Other things you should take care of
The Prophet (ﷺ) made a bond of brotherhood between Salman and Abu Ad-Darda.' Salman paid a visit to Abu Ad-Darda' and found Um Ad-Darda' dressed in shabby clothes and asked her why she was in that state. She replied, "Your brother Abu Ad-Darda' is not interested in (the luxuries of) this world." In the meantime Abu Ad-Darda' came and prepared a meal for Salman. Salman requested Abu Ad- Darda' to eat (with him), but Abu Ad-Darda' said, "I am fasting." Salman said, "I am not going to eat unless you eat." So, Abu Ad-Darda' ate (with Salman). When it was night and (a part of the night passed), Abu Ad-Darda' got up (to offer the night prayer), but Salman told him to sleep and Abu Ad- Darda' slept. After sometime Abu Ad-Darda' again got up but Salman told him to sleep. When it was the last hours of the night, Salman told him to get up then, and both of them offered the prayer. Salman told Abu Ad-Darda', "Your Lord has a right on you, your soul has a right on you, and your family has a right on you; so you should give the rights of all those who has a right on you." Abu Ad- Darda' came to the Prophet (ﷺ) and narrated the whole story. The Prophet (ﷺ) said, "Salman has spoken the truth." (Sahih al-Bukhari)
Note that this hadith has other sources where the bold statement clearly is referred to as the words of the Prophet () and could be used as an evidence to say that you shouldn't go with your body and strength beyond their limits and should have a rest when you need it, you shouldn't do more worship then your body is able to perform. Which is the statement of this hadith:
The Prophet (ﷺ) said, "Religion is very easy and whoever overburdens himself in his religion will not be able to continue in that way. So you should not be extremists, but try to be near to perfection and receive the good tidings that you will be rewarded; and gain strength by worshipping in the mornings, the afternoons, and during the last hours of the nights." (Sahih al-Bukhari)
The prophet () also got upset from some sahaba who tried to follow his worship or restrain from things that have been made lawful for them saying:
What has happened to these people that they say so and so, whereas I observe prayer and sleep too; I observe fast and suspend observing them; I marry women also? And he who turns away from my Sunnah, he has no relation with Me. (Sahih Muslim)
'Abdullah ibn 'Amr ibn al'Aas was one of them -he was young and felt strong at the time- and here you may read what the Prophet () advised him:
Allah's Messenger (ﷺ) said to me, "O 'Abdullah! Have I not been informed that you fast during the day and offer prayers all the night." 'Abdullah replied, "Yes, O Allah's Messenger (ﷺ)!" The Prophet (ﷺ) said, "Don't do that; fast for few days and then give it up for few days, offer prayers and also sleep at night, as your body has a right on you, and your wife has a right on you, and your guest has a right on you. And it is sufficient for you to fast three days in a month, as the reward of a good deed is multiplied ten times, so it will be like fasting throughout the year." I insisted (on fasting) and so I was given a hard instruction. I said, "O Allah's Messenger (ﷺ)! I have power." The Prophet (ﷺ) said, "Fast like the fasting of the Prophet (ﷺ) David and do not fast more than that." I said, "How was the fasting of the Prophet (ﷺ) of Allah, David?" He said, "Half of the year," (i.e. he used to fast on every alternate day). Afterwards when `Abdullah became old, he used to say, "It would have been better for me if I had accepted the permission of the Prophet (which he gave me i.e. to fast only three days a month). (Sahih al-Bukhari)
And you should follow this advise, don't do anything which would harm you, good deeds are the best if you could stick on them and keep doing them your whole life! Note that this hadith could be used as an evidence for taking enough sleep or rest to be able to fulfil your worship and worldly tasks.
Nevertheless it is true that performing extra worships is very recommended (as this hadith indicates), but if you do the ordered worships in a good way that is the best and a solid basis (see this sahih hadith). So the best solution is a good midway.
My advise for you is perform the ordered acts of worship, if you want pray the fajr sunnah and the witr prayer or a-shaf'a (2 raka' set(s) after 'isha) and witr (single raka'a or 3 raka'a after 'isha) for now, once you feel at ease you may chose some additional optional worships, but don't start too heavily at the beginning, as at the end you may realize that your body can't afford this.