The decision to write 

>The earthquake, along with its subsequent aftershocks, has created an atmosphere of panic among the city's residents. 

instead of the simpler 

>The earthquake and its subsequent aftershocks have created an atmosphere of panic among the city's residents. 

reflects a choice by the author to stress the idea that that the earthquake alone sufficed to create an atmosphere of panic in the populace. By putting the aftershocks into what amounts to a parenthetical phrase, the author emphasizes the original earthquake as the main factor in the terrorizing of the citizenry, with (oh yes) the aftershocks as relevant factors, too.

If you interpret "along with" as being nothing more than a fancy way of saying "and," you give yourself grounds for using *have* instead of *has*—but you also call into question the author's judgment in using that more convoluted wording and especially in setting off the "along with its subsequent aftershocks" phrase with commas.

The converse problem would arise if the author had written the sentence this way:

>The earthquake—and its subsequent aftershocks—has/have created an atmosphere of panic among the city's residents.

If the aftershocks weren't an afterthought, the author would have done better to dispense with the em-dashes and to treat the earthquake and the aftershocks as a joint subject responsible in combination for the atmosphere of panic. But by breaking out the "and its subsequent aftershocks" phrase, it seems to me, the author assigns primary credit to the earthquake and only secondary or tertiary credit to the aftershocks. Though I wouldn't want to change *have* to *has* in that case (if the rest of the wording and punctuation remained unchanged), I would want to change *and* to *along with* or *as well as* or *reinforced by* or *followed by*, and then choose *has* over *have*.

So far, I've been discussing the written form of the example sentences. In spoken English, the punctuation disappears and you have to gauge the appropriate form of the verb by the pauses, changes in intonation, or other signals accompanying the statement (thanks to Araucaria for pointing out that intonation is a crucial factor; for a discussion of intonation contours, Araucaria recommends Sandra Döring, "[Quieter, faster, lower, and set off by pauses?](https://books.google.co.uk/books?id=_aY5AAAAQBAJ&pg=PA289&lpg=PA289&dq=intonation+parentheticals+phonetics&source=bl&ots=QwiYEj6qG0&sig=FRtcCbMq0kg89RuzxGz2DTkbnq4&hl=en&sa=X&ved=0ahUKEwjZ1eP036_KAhWEiRoKHdFSCZIQ6AEIOzAE#v=onepage&q=%22intonation%20contours%22&f=false)," in Nicole Dehé & Yordanka Kavalova, eds, *Parentheticals* [2007]). But if I were hearing the OP's example read aloud, I would take "along with" to signal a parenthetical break from the main subject and its associated verb, and I would expect the primary subject "earthquake" to take a singular verb.