Unwanted item in reference list when using crossref with biber

The crossref field is about more than just data inheritance. It is also about establishing a certain parent-child relation between entries (cf. the xref field, which only models this parent-child relation without data inheritance).

One feature of this parent-child relation is that a parent entry is automatically added to the bibliography if it is referred to by a certain number of children (even if it is not cited explicitly). The exact number of child references can be controlled with the mincrossrefs option. Its default value is 2, meaning that a parent entry is added to the bibliography if it is referred to by at least two (different) child entries. That is the case in your example: myjournal is referenced by myarticle1 and myarticle2.

One way around that would be to set mincrossrefs to a higher (maybe unreasonably high) value such as 999 as suggested by Manuel Weinkauf in the comments.

documentclass{article}

usepackage[backend=biber, style=alphabetic, mincrossrefs=999]{biblatex}

begin{filecontents}{jobname.bib}
@article{myjournal,
  journaltitle = {Journal of Interesting Things},
  publisher    = {Someone},
}
@article{myarticle1,
  crossref = {myjournal},
  title    = {That thing},
  author   = {Martypants, Susan},
  year     = {2019},
}
@article{myarticle2,
  crossref = {myjournal},
  title    = {That other thing},
  author   = {Rofessor, Peter},
  year     = {2020},
}
end{filecontents}
addbibresource{jobname.bib}

begin{document}
autocite{myarticle1,myarticle2}

printbibliography
end{document}

---

An alternative would be to tell biblatex that myjournal is only a data container and not an entry that could appear in the bibliography in its own right. That is done by adding options = {dataonly}, to the entry. This is not unlike Cicada's suggestion of options={skipbib=true},, but slightly more rigorous (since it will also avoid label creation, which fails here anyway, to be fair). With this solution myjournal doesn't even appear in the bibliography when cited explicitly, though.

documentclass{article}

usepackage[backend=biber, style=alphabetic]{biblatex}

begin{filecontents}{jobname.bib}
@article{myjournal,
  journaltitle = {Journal of Interesting Things},
  publisher    = {Someone},
  options      = {dataonly},
}
@article{myarticle1,
  crossref = {myjournal},
  title    = {That thing},
  author   = {Martypants, Susan},
  year     = {2019},
}
@article{myarticle2,
  crossref = {myjournal},
  title    = {That other thing},
  author   = {Rofessor, Peter},
  year     = {2020},
}
end{filecontents}
addbibresource{jobname.bib}

begin{document}
autocite{myarticle1,myarticle2}

printbibliography
end{document}

---

If you don't want to establish this additional parent-child relation it may be better to choose a different tool for the job: Cicada suggested @xdata containers in the comments. The biblatex documentation explains xdata as follows (§2.2.3 Special Fields, p. 31)

This field inherits data from one or more @xdata entries. Conceptually, the xdata field is related to crossref and xref: crossref establishes a logical parent/child relation and inherits data; xref establishes as logical parent/child relation without inheriting data; xdata inherits data without establishing a relation. The value of the xdata may be a single entry key or a separated list of keys. See §3.13.6 for further details.

And that seems a great fit: xdata is crossref sans the parent-child relation that caused the undesired behaviour in the first place.

It should be noted, however, that @xdata entries can't appear in the bibliography themselves and can't usefully be cited. Furthermore, the field inheritance with @crossref can take into account the entry types of the parent and child entries and can set up rules like the title field of a @collection parent is inherited as booktitle to an @incollection child. This is not possible (and does not make sense) for @xdata.

documentclass{article}

usepackage[backend=biber, style=alphabetic]{biblatex}

begin{filecontents}{jobname.bib}
@xdata{myjournal,
  journaltitle = {Journal of Interesting Things},
  publisher    = {Someone},
}
@article{myarticle1,
  xdata    = {myjournal},
  title    = {That thing},
  author   = {Martypants, Susan},
  year     = {2019},
}
@article{myarticle2,
  xdata    = {myjournal},
  title    = {That other thing},
  author   = {Rofessor, Peter},
  year     = {2020},
}
end{filecontents}
addbibresource{jobname.bib}

begin{document}
autocite{myarticle1,myarticle2}

printbibliography
end{document}

---

In this particular case all standard styles will ignore the publisher field for @articles, so you are only inheriting one field, namely the journal(title). Single-field inheritance can also be modelled with @string entries. (But of course that is not an option if you want to inherit multiple fields at once.)

documentclass{article}

usepackage[backend=biber, style=alphabetic]{biblatex}

begin{filecontents}{jobname.bib}
@string{myjournal = {Journal of Interesting Things}}
@article{myarticle1,
  journal  = myjournal,
  title    = {That thing},
  author   = {Martypants, Susan},
  year     = {2019},
}
@article{myarticle2,
  journal  = myjournal,
  title    = {That other thing},
  author   = {Rofessor, Peter},
  year     = {2020},
}
end{filecontents}
addbibresource{jobname.bib}

begin{document}
autocite{myarticle1,myarticle2}

printbibliography
end{document}

All of the posted example produce