A defendant has the right to be tried by his peers. A group of the defendant's peers want to attend the trial as these peers. How do we confront the judge with our rights to be those peers? Peers are not court appointed jury.
A defendant has the right to be tried by his peers.
In the U.S., this is an incorrect belief. A defendant does not has the right to be tried by his peers in the U.S.
The "jury of his peers" language is a legacy of English law in the days when aristocrats were entitled to a jury of aristocrats rather than commoners, while commoners were entitled to a jury of commoners.
The sole legacy of that in U.S. law is in court-martials in which officers are entitled to have their cases heard by a panel of fellow officers, rather than by a panel of active duty military personnel generally.
Outside of court-martials in the U.S., the "jury of his peers" concept was eliminated not later than the time when the current U.S. constitution was adopted (in 1789) which eliminated hereditary titles of nobility, or when 6th Amendment to the Bill of Rights was adopted (as applicable in federal criminal cases) which was adopted in 1791.
Instead, the Courts have interpreted the 6th Amendment right to trial by jury, which has now been applied to state and local governments as well, to require that the jury be drawn from a fair cross-section of the community (regardless of what an individual jury actually ends up as) and to have people who are conflicted or biased removed from the jury.
From your user name, I guess you are in the US. So the relevant text would be the 6th Amendment,
In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury [...]
There are exceptions to the trial being public, either at the request of the defendant or at the request of the prosecution/government. Also, being public does not mean that all prospective attendants may watch, just that some visitors and press are allowed in, up to capacity.
The legal system tries to assure an impartial jury by not picking them from the visitors. The way to be picked varies from state to state, it starts with voter records, driving licenses, etc. and then a random pick, followed by attempts to exclude those with a connection to the case.
The relevant provision in the US federal constitution is the Sixth Amendment, which reads:
In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law.
Note that this says nothing about peers. It requires the jury to be "impartial", and to come from the same area where the crime occurred.
The phrase "Jury of his peers" derives from the English Magna Carta (Great Charter), specifically from Chapter 39 of the 1215 version. A translation into modern English of this posted by the British Library reads:
(39) No free man shall be seized or imprisoned, or stripped of his rights or possessions, or outlawed or exiled, or deprived of his standing in any way, nor will we proceed with force against him, or send others to do so, except by the lawful judgment of his equals or by the law of the land.
This demand was made of King John by the Barons, who objected to being judged by those of inferior social status. Originally it applied primarily to judges, not juries. But it was not enforced as intended. The clause "or by the law of the land" was soon taken to man that as long as a judge ruled according to established law, the judge could be of common birth. (see *Magna Carta by J. C. Holt, ISBn 978-1107471573; Se also The Law of the Land by Charles Rembar) Later chapter 39 led to the right of British Peers of the Realm to be tried only by the House of lords, a right that persisted in the UK until well into the 20th century. But there has never been that sort of right in the US since it became a nation.
Some older state constitutions do preserve the words "jury of peers". For example The Virginia Constution provides (in Art. I, § 8) that:
In criminal prosecutions a man has a right to demand the cause and nature of his/her accusation, to be confronted with the accusers and witnesses, and to call for evidence in his favor, and s/he must enjoy the right to a speedy and public trial, by an impartial jury of his/her vicinage, without whose unanimous consent s/he cannot be found guilty. S/he shall not be deprived of life or liberty, except by the law of the land or the judgment of his peers, nor be compelled in any criminal proceeding to give evidence against himself, nor be put twice in jeopardy for the same offense.
But this, and similar provisions elsewhere, have been held to mean a jury of citizens, not specially selected to include or exclude any race, profession, or other special group. Indeed any such selection would render the trial invalid under the Sixth Amendment, and the Due Process clause of the Fifth or Fourteenth.
There is no process by which a group may present itself to a judge as the "peers" and ask to be seated as the jury in a particular case, nor by which the defendant may present a group as his or her "peers". A defendant may object to a particular person believed to be biased or otherwise ineligible, and may object to a selection process s/he thinks unfair or biased. But a defendant may not demand and obtain a jury that more closely resembles himself or herself than a widely representative cross-section of the community.
Law.com says of the jury guarantee:
...This has been interpreted by courts to mean that the available jurors include a broad spectrum of the population, particularly of race, national origin and gender. Jury selection may include no process which excludes those of a particular race or intentionally narrows the spectrum of possible jurors. It does not mean that women are to be tried by women, Asians by Asians, or African Americans by African Americans.
The LII page says of the Sixth Amendment provision:
This right can be found in the Sixth Amendment of the U.S. Constitution where it states, “the accused shall enjoy the right to a speedy and public trial, by an impartial jury.” See Impartial Jury. The purpose of this provision is to ensure that a jury’s verdict is not tainted by biases that jurors may harbor before being presented with the evidence of the particular case. Readily recognized biases include gender, race, sexual orientation, nationality, etc. To exclude potentially biased jurors, either party to the suit may use a peremptory challenge during the jury selection process.