In a Sandhyavandanam at what juncture does turiiya arghyam occur? Does it occur before or after the respective Sandhyavandanam periods (Sunrise and Sunset)? Is there any stipulation that Sandhyavandanam is to be performed only with a certain time window before or after Sunrise and Sunset? For example, can the morning Sandhyavandanam can be performed either at 4 AM or 11 AM?

In a Sandhyavandanam, 3 arghyams must be offered before Sunrise. If the Sun has already risen, it means is past the time for Sandhyavandanam; when done so, a fourth arghyam called turiiya arghyam is offered as an atonement.
If Sandhyavandanm is performed before Sunrise, no need to offer turiiya arghyam.
Similarly, if 3 arghyams are offered before Sunset, turiiya arghyam is not offered.
Both Sunrise and Sunset timing varies frequently and also at different times of the year such as summer, monsoon season, etc.; given this, it will be difficult to indicate the time for this.
Hence, consult a panchangam, determine Sunrise and Sunset and offer 3 arghyams before Sunrise and Sunset; when done so, no need to offer turiiya arghyam.
Sandhyavandanam cannot be performed at 4 AM as it must be commenced before Sunrise and concluded with upasthanam after Sunrise. Arghyam must be offered before Sunrise and upasthanam is performed after Sunrise.
Doing Sandhyavandanam at 4 AM is considered untimely karma and has no value as a result. One must again perform Sandhyavandanam.
Due to compulsion when one is away or delayed during Sandhyavandanam time, it must be performed at 11 AM by offering turiiya arghyam.